Relevant bibliographies by topics / Curvature functionals

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Curvature functionals'

Author: Grafiati
Published: 14 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Curvature functionals"

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Shcherbakov, Eugeniy, and Mikhail Shcherbakov. "ON THE GAUSSIAN CURVATURE FUNCTIONAL IN THE CLASS OF SURFACES OF POSITIVE GAUSSIAN CURVATURE." Mathematical Physics and Computer Simulation 27, no. 3 (2024): 60–66. https://doi.org/10.15688/mpcm.jvolsu.2024.3.5.

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The paper establishes the form of the Gaussian curvature functional defined on the class of infinitely differentiable horizontal surfaces of positive Gaussian curvature. With respect to admissible surfaces, it is assumed that they admit a global semi-geodetic parametrization. The paper proves that the first variation of the functional on the class of variations of admissible surfaces admitting connections between the coefficients of the first quadratic form and their geodesic lines similar to the axisymmetric case is determined by the Gaussian curvature of the varied surface. The consideration
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Ivochkina, N. M. "Minimization of functionals generating curvature operators." Journal of Soviet Mathematics 62, no. 3 (1992): 2741–46. http://dx.doi.org/10.1007/bf01670999.

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Sheng, Weimin, and Lisheng Wang. "Variational properties of quadratic curvature functionals." Science China Mathematics 62, no. 9 (2018): 1765–78. http://dx.doi.org/10.1007/s11425-017-9232-6.

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Sarkar, Prakash. "Quantifying the Cosmic Web using the Shapefinder diagonistic." Proceedings of the International Astronomical Union 11, S308 (2014): 250–53. http://dx.doi.org/10.1017/s1743921316009960.

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AbstractOne of the most successful method in quantifying the structures in the Cosmic Web is the Minkowski Functionals. In 3D, there are four minkowski Functionals: Area, Volume, Integrated Mean Curvature and the Integrated Gaussian Curvature. For defining the Minkowski Functionals one should define a surface. We have developed a method based on Marching cube 33 algorithm to generate a surface from a discrete data sets. Next we calculate the Minkowski Functionals and Shapefinder from the triangulated polyhedral surface. Applying this methodology to different data sets , we obtain interesting r
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Brozos‐Vázquez, Miguel, Sandro Caeiro‐Oliveira, and Eduardo García‐Río. "Critical metrics for all quadratic curvature functionals." Bulletin of the London Mathematical Society 53, no. 3 (2021): 680–85. http://dx.doi.org/10.1112/blms.12448.

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Kuwert, Ernst, Tobias Lamm, and Yuxiang Li. "Two-dimensional curvature functionals with superquadratic growth." Journal of the European Mathematical Society 17, no. 12 (2015): 3081–111. http://dx.doi.org/10.4171/jems/580.

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Joshi, Pushkar, and Carlo Séquin. "Energy Minimizers for Curvature-Based Surface Functionals." Computer-Aided Design and Applications 4, no. 5 (2007): 607–17. http://dx.doi.org/10.1080/16864360.2007.10738495.

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von der Mosel, Heiko. "Nonexistence results for extremals of curvature functionals." Archiv der Mathematik 69, no. 5 (1997): 427–34. http://dx.doi.org/10.1007/s000130050141.

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Biondi, Biondo. "Velocity estimation by image-focusing analysis." GEOPHYSICS 75, no. 6 (2010): U49—U60. http://dx.doi.org/10.1190/1.3506505.

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Migration velocity can be estimated from seismic data by analyzing, focusing, and defocusing of residual-migrated images. The accuracy of these velocity estimates is limited by the inherent ambiguity between velocity and reflector curvature. However, velocity resolution improves when reflectors with different curvatures are present. Image focusing is measured by evaluating coherency across structural dips, in addition to coherency across aperture/azimuth angles. The inherent ambiguity between velocity and reflector curvature is directly tackled by introducing a curvature correction into the co
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Bernardini, Marco. "New rigidity results for critical metrics of some quadratic curvature functionals." Advances in Geometry 25, no. 1 (2025): 1–12. https://doi.org/10.1515/advgeom-2024-0032.

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Abstract We prove a new rigidity result for metrics defined on closed smooth n-manifolds that are critical for the quadratic functional 𝔉 t , which depends on the Ricci curvature Ric and the scalar curvature R, and that satisfy a pinching condition of the form Sec > ε R, where ε is a function of t and n, while Sec denotes the sectional curvature. In particular, we show that Bach-flat metrics with constant scalar curvature satisfying Sec > 1 48 $\begin{array}{} \displaystyle \frac{1}{48} \end{array}$ R are Einstein and, by a known result, are isometric to 𝕊4, ℝℙ4 or ℂℙ2.
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Dissertations / Theses on the topic "Curvature functionals"

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Mondino, Andrea. "The Willmore functional and other L^p curvature functionals in Riemannian manifolds." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4840.

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Using techniques both of non linear analysis and geometric measure theory, we prove existence of minimizers and more generally of critical points for the Willmore functional and other $L^p$ curvature functionals for immersions in Riemannian manifolds. More precisely, given a $3$-dimensional Riemannian manifold $(M,g)$ and an immersion of a sphere $f:\Sp^2 \hookrightarrow (M,g)$ we study the following problems. 1) The Conformal Willmore functional in a perturbative setting: consider $(M,g)=(\Rtre,\eu+\epsilon h)$ the euclidean $3$-space endowed with a perturbed metric ($h=h_{\mu\nu}$ is a s
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PARRILLO, ANTONELLA. "Analytical and computational study of curvature depending functionals in image segmentation." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/689.

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In questa tesi sono stati trattati problemi di segmentazione dell'immagine mediante strumenti di analisi variazionale. Ho studiato due funzionali contenenti integrali di funzioni dipendenti dalla curvatura degli elementi di una famiglia di curve $C$ approssimante i contorni di una data immagine, la lunghezza di esse e il numero dei loro punti finali. Per uno dei due funzionali ho calcolato il sistema delle equazioni di Eulero e, usando uno schema iterativo basato sulle differenze finite, ho effettuato esperimenti al computer su alcune immagini.<br>In the present thesis we study variational p
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Winklmann, Sven. "Krümmungsabschätzungen für stabile Extremalen parametrischer Funktionale / Curvature estimates for stable extremals of parametric functionals." Gerhard-Mercator-Universitaet Duisburg, 2004. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-03192004-115454/.

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We consider immersed hypersurfaces in euclidean $R^{n+1}$ which are stable with respect to an elliptic parametric functional with integrand $F=F(N)$ depending on normal directions only. We prove an integral curvature estimate provided that $F$ is sufficiently close to the area integrand, extending the classical curvature estimate of Schoen, Simon and Yau for stable minimal hypersurfaces in $R^{n+1}$. As a crucial point of our analysis we derive a generalized Simons inequality for the laplacian of the length of a weighted second fundamental form with respect to an abstract metric associated wit
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Käfer, Bastian [Verfasser], der Mosel Heiko Akademischer Betreuer] von, Alfred [Akademischer Betreuer] [Wagner, and Pawel [Akademischer Betreuer] Strzelecki. "Scale-invariant geometric curvature functionals, and characterization of Lipschitz- and $C^1$-submanifolds / Bastian Käfer ; Heiko von der Mosel, Alfred Wagner, Pawel Strzelecki." Aachen : Universitätsbibliothek der RWTH Aachen, 2021. http://d-nb.info/1239566719/34.

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Silva, Adam Oliveira da. "Rigidez de métricas críticas para funcionais riemannianos." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25969.

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SILVA, Adam Oliveira da. Rigidez de métricas críticas para funcionais riemannianos. 2017. 78 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-19T19:08:04Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 481005 bytes, checksum: 2bdfc6ab68b042a5cfd4f67caf1e21e4 (MD5)<br>Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia, Estou devolvendo a Tese de ADAM OLIVEIRA DA SILVA, para que o arquivo seja substituído, pois o aluno já veio na BCM e orientei quais eram as correções a ser
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Dalphin, Jérémy. "Étude de fonctionnelles géométriques dépendant de la courbure par des méthodes d'optimisation de formes. Applications aux fonctionnelles de Willmore et Canham-Helfrich." Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0167/document.

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En biologie, lorsqu'une quantité importante de phospholipides est insérée dans un milieu aqueux, ceux-Ci s'assemblent alors par paires pour former une bicouche, plus communément appelée vésicule. En 1973, Helfrich a proposé un modèle simple pour décrire la forme prise par une vésicule. Imposant la surface de la bicouche et le volume de fluide qu'elle contient, leur forme minimise une énergie élastique faisant intervenir des quantités géométriques comme la courbure, ainsi qu'une courbure spontanée mesurant l'asymétrie entre les deux couches. Les globules rouges sont des exemples de vésicules su
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Guo, Li. "Shape blending using discrete curvature-variation functional /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?IEEM%202005%20GUO.

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ALESSANDRONI, ROBERTA. "Evolution of hypersurfaces by curvature functions." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/661.

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Consideriamo un'ipersuperficie liscia di ℝⁿ⁺¹, con n≥2, e la sua evoluzione secondo una classe di flussi geometrici. La velocità di questi flussi ha direzione normale alla superficie e il modulo è una funzione simmetrica delle curvature principali. Inizialmente mostriamo alcune proprietà generali di questi flussi e calcoliamo l'equazione di evoluzione per una generica funzione omogenea delle curvature principali. In particolare applichiamo il flusso con velocità S=(H/(logH)), dove H è la curvatura media a meno di una costante, ad una superficie con curvatura media positiva per ottenere delle
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Evangelista, Israel de Sousa. "Compact almost Ricci soliton, critical metrics of the total scalar curvature functional and p-fundamental tone estimates." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/23920.

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EVANGELISTA, I. S. Compact almost Ricci soliton, critical metrics of the total scalar curvature functional and p-fundamental tone estimates. 2017. 75 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-07-10T12:41:32Z No. of bitstreams: 1 2017_tese_isevangelista.pdf: 618771 bytes, checksum: 7e4bb8d9fd8825ef347e309171075037 (MD5)<br>Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-07-10T14:06:18Z (GMT) No. of bitstreams: 1 2017_tese_isevangelista.pdf: 618771 byte
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Buckland, John A. (John Anthony) 1978. "Mean curvature flow with free boundary on smooth hypersurfaces." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/5809.

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Books on the topic "Curvature functionals"

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Yang, Kichoon. Complete Minimal Surfaces of Finite Total Curvature. Springer Netherlands, 1994.

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Wu, K. Chauncey. Free vibration of hexagonal panels simply supported at discrete points. National Aeronautics and Space Administration, Langley Research Center, 1991.

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Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. American Mathematical Society, 2015.

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Wentworth, Richard A., Duong H. Phong, Paul M. N. Feehan, Jian Song, and Ben Weinkove. Analysis, complex geometry, and mathematical physics: In honor of Duong H. Phong : May 7-11, 2013, Columbia University, New York, New York. American Mathematical Society, 2015.

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Metrics of positive scalar curvature and generalised Morse functions. American Mathematical Society, 2011.

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Tretkoff, Paula. Riemann Surfaces, Coverings, and Hypergeometric Functions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0003.

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This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and notes that an automorphism of a Riemann surface is a biholomorphic map of the Riemann surface onto itself. It then describes a Riemannian metric and the Gauss-Bonnet theorem, which can be interpreted as a relation between the Gaussian curvature of a compact Riemann surface X and its Euler characteristic. It also examines the behavior of the Euler number under finite covering, along with finite subgroup
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Briggs, Carey. General Expressions for the 5-Dimensional Riemann-Christoffel, Ricci, and Einstein Curvature Tensors and Riemann Curvature Scalar Allowing for Non-Vanishing Torsion and Arbitrary Functional Dependence on the Fifth Dimension. Lulu Press, Inc., 2021.

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Free vibration of hexagonal panels simply supported at discrete points. National Aeronautics and Space Administration, Langley Research Center, 1991.

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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator
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Gilad-Gutnick, Sharon, Rohan Varma, and Pawan Sinha. The Bogart Effect. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0089.

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While a geometry-based eye-gaze estimation strategy has been the basis of many theories regarding the direction of one’s gaze, such a strategy relies on relatively detailed curvature information and therefore functions suboptimally under low-resolution viewing conditions. Partly in response to this concern, the past decade has seen the rise of luminance-based theories of eye-gaze estimation. The idea of luminance-based estimation of gaze direction arose from the observation that contrast negation affects eye-gaze perception, and an early demonstration and possible explanation for this phenomen
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Book chapters on the topic "Curvature functionals"

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Viaclovsky, Jeff. "Critical metrics for Riemannian curvature functionals." In Geometric Analysis. American Mathematical Society, 2016. http://dx.doi.org/10.1090/pcms/022/05.

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Blair, David E. "Curvature Functionals on Spaces of Associated Metrics." In Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4757-3604-5_10.

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Blair, David E. "Curvature Functionals on Spaces of Associated Metrics." In Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4959-3_10.

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Nitsche, Johannes C. C. "Periodic Surfaces That are Extremal for Energy Functionals Containing Curvature Functions." In Statistical Thermodynamics and Differential Geometry of Microstructured Materials. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-8324-6_6.

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Dineen, Seán. "Curvature." In Functions of Two Variables. Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-3250-1_14.

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Jost, Jürgen. "Convex functions and centers of mass." In Nonpositive Curvature: Geometric and Analytic Aspects. Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8918-6_3.

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Sunada, Toshikazu. "L-functions in geometry and some applications." In Curvature and Topology of Riemannian Manifolds. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075662.

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Shiohama, Katsuhiro. "Critical points of Busemann functions on complete open surfaces." In Curvature and Topology of Riemannian Manifolds. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075661.

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Pinkall, Ulrich, and Oliver Gross. "Variations of Surfaces." In Compact Textbooks in Mathematics. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-39838-4_12.

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AbstractWe derive the basics of Vector Calculus on surfaces and explore variations of surfaces. In particular, we compute the variational derivative of the area form $$\det $$ det and of the shape operator A. We show that the critical points of the area functional are the surfaces with mean curvature $$H=0$$ H = 0 .
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Alexander, Stephanie B., and William A. Karr. "Space-Time Convex Functions and Sectional Curvature." In Lorentzian Geometry and Related Topics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66290-9_2.

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Conference papers on the topic "Curvature functionals"

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Martin, Victor F., Luis Landesa, Jorge A. Tobon Vasquez, Jose M. Taboada, and Francesca Vipiana. "Origami Basis Functions for Modeling the Curvature Correction in H-refinement Methods via Method of Moments." In 2024 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2024. http://dx.doi.org/10.1109/iceaa61917.2024.10701935.

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NETERENKO, V. V., A. FEOLI, and G. SCARPETTA. "FUNCTIONALS LINEAR IN CURVATURE AND STATISTICS OF HELICAL PROTEINS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702883_0047.

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Xu, Leidong, Kiarash Naghavi Khanghah, and Hongyi Xu. "Design of Mixed-Category Stochastic Microstructures: A Comparison of Curvature Functional-Based and Deep Generative Model-Based Methods." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-114601.

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Abstract Bridging the gaps among various categories of stochastic microstructures remains a challenge in the design representation of microstructural materials. Each microstructure category requires certain unique mathematical and statistical methods to define the design space (design representation). The design representation methods are usually incompatible between two different categories of stochastic microstructures. The common practice of pre-selecting the microstructure category and the associated design representation method before conducting rigorous computational design limits the de
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Rajidi, Shashidhar Reddy, Abhay Gupta, and Satyajit Panda. "Supersonic Aerodynamic Instability Characteristics of Bidirectional Porous Functionally Graded Panel." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59346.

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Abstract The objective to alleviate the detrimental effects of supersonic flutter of aerospace structures necessitates the development of advanced composite materials. Porous functionally graded materials are viable alternatives to replace the metal/alloys used for critical components. The present work investigates the supersonic flutter characteristics of hinged-hinged panel for the porosity grading across the thickness and/or along the streamwise direction. Also, the possibility to alleviate the detrimental effects is investigated through the study of influence of streamwise and spanwise cur
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Knippenberg, Christopher H., Oliver J. Myers, and Christopher Nelon. "Functional Description for Thick Bistable Carbon Fiber Laminates With Rayleigh-Ritz, Abaqus, and Experiments." In ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/smasis2020-2293.

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Abstract Composite laminates constructed in an asymmetric layup orientation of [0i, 90i], i &amp;gt; 0, exhibit two stable equilibrium positions and may be actuated to snap from a primary cure shape to an inversely related secondary stable shape. This study aims to aid in developing a comprehensive description of thick bistable laminates, whose increased thickness risks the loss of bistability, through previously established analytical approaches and verification via experimentation. The principle of minimum potential energy is applied to two materials and analyzed using the Rayleigh-Ritz mini
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Yoshida, Norimasa, and Takafumi Saito. "Planar Curves-based on Explicit Bézier Curvature Functions." In CAD'19. CAD Solutions LLC, 2019. http://dx.doi.org/10.14733/cadconfp.2019.323-327.

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BRITO, F., H. L. LIU, U. SIMON, and C. P. WANG. "HYPERSURFACES IN SPACE FORMS WITH SOME CONSTANT CURVATURE FUNCTIONS." In Geometry and Topology of Submanifolds IX. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812817976_0006.

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Lehky, Sidney R., and Terrence J. Sejnowski. "Extracting 3-D curvatures from images of surfaces using a neural network." In OSA Annual Meeting. Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.mh3.

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A network which extracts principal curvatures and orientations from images of simple surfaces using shading information was constructed with the backpropagation learning algorithm.1 The surfaces were elliptic paraboloids with a parabolic cross section in depth, an elliptical cross section in the fronto-parallel plane, and a Lambertian reflectance function. The network finds the principal curvatures and directions at the centers of the surfaces over a wide range of values for those parameters, independent of illumination direction and the location of the center. Input is mediated by convolving
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Torselletti, Enrico, Luigino Vitali, Roberto Bruschi, Erik Levold, and Leif Collberg. "Submarine Pipeline Installation Joint Industry Project: Global Response Analysis of Pipelines During S-Laying." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92377.

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The development of deep water gas fields using trunklines to carry the gas to the markets is sometime limited by the feasibility/economics of the construction phase. In particular there is market for using S-lay vessel in water depth larger than 1000m. The S-lay feasibility depends on the applicable tension at the tensioner which is a function of water depth, stinger length and stinger curvature (for given stinger length by its curvature). This means that, without major vessel up-grading and to avoid too long stingers that are prone to damages caused by environmental loads, the application of
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Leamy, Michael J. "Dynamic Finite Element Modeling of Carbon Nanotubes Using an Intrinsic Formulation." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84482.

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This article presents an efficient explicit dynamic formulation for modeling curved and twisted Carbon Nanotubes (CNT’s) based on a recently-developed intrinsic beam description (i.e. the dynamic state given by curvatures, strains, and velocities only) [Hodges, 2003] together with a finite element discretization incorporating atomistic potentials. This approach offers several advantages primarily related to the model’s computational efficiency: 1) the resulting partial differential equations governing motion are in first-order form (i.e. have first-order time derivatives only), 2) the system n
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Reports on the topic "Curvature functionals"

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Diewert, W. Erwin, and T. J. Wales. Flexible Functional Forms and Global Curvature Conditions. National Bureau of Economic Research, 1989. http://dx.doi.org/10.3386/t0040.

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Stuedlein, Armin, Ali Dadashiserej, and Amalesh Jana. Models for the Cyclic Resistance of Silts and Evaluation of Cyclic Failure during Subduction Zone Earthquakes. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, 2023. http://dx.doi.org/10.55461/zkvv5271.

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This report describes several advances in the cyclic failure assessment of silt soils with immediate and practical benefit to the geotechnical earthquake engineering profession. First, a database of cyclic loading test data is assembled, evaluated, and used to assess trends in the curvature of the CRR-N (cyclic resistance ratio - the number of equivalent cycles) relationship. This effort culminated in a plasticity index-dependent function which can be used to estimate the exponent b in the power law describing cyclic resistance, and may be used to estimate the cyclic resistance of silt soils a
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