Academic literature on the topic 'Laplace-Beltrami-Operator'

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Journal articles on the topic "Laplace-Beltrami-Operator"

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XU, GUOLIANG. "DISCRETE LAPLACE–BELTRAMI OPERATOR ON SPHERE AND OPTIMAL SPHERICAL TRIANGULATIONS." International Journal of Computational Geometry & Applications 16, no. 01 (2006): 75–93. http://dx.doi.org/10.1142/s0218195906001938.

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In this paper we first modify a widely used discrete Laplace-Beltrami operator proposed by Meyer et al over triangular surfaces, and then we show that the modified discrete operator has some convergence properties over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace-Beltrami operator is constructed. Optimal hierarchical spherical triangulations are also given. Truncation error bounds of the discrete Laplace-Beltrami operator over the constructed triangulations are provided.
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Hashiguchi, Hiroki, Shigekazu Nakagawa, and Naoto Niki. "Simplification of the Laplace–Beltrami operator." Mathematics and Computers in Simulation 51, no. 5 (2000): 489–96. http://dx.doi.org/10.1016/s0378-4754(99)00139-1.

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Petronetto, F., A. Paiva, E. S. Helou, D. E. Stewart, and L. G. Nonato. "Mesh-Free Discrete Laplace-Beltrami Operator." Computer Graphics Forum 32, no. 6 (2013): 214–26. http://dx.doi.org/10.1111/cgf.12086.

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Caissard, Thomas, David Coeurjolly, Jacques-Olivier Lachaud, and Tristan Roussillon. "Laplace–Beltrami Operator on Digital Surfaces." Journal of Mathematical Imaging and Vision 61, no. 3 (2018): 359–79. http://dx.doi.org/10.1007/s10851-018-0839-4.

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OLIVIER, D., and G. VALENT. "MULTIPLICATIVE RENORMALIZABILITY AND THE LAPLACE-BELTRAMI OPERATOR." International Journal of Modern Physics A 06, no. 06 (1991): 955–76. http://dx.doi.org/10.1142/s0217751x91000526.

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For some rank 1 non-linear σ models we prove that a necessary and sufficient condition of multiplicative renormalizability for composite fields is that they should be eigenfunctions of the coset Laplace-Beltrami operator. These eigenfunctions span the irreducible representation space of the isometry group and may be finite- or infinite-dimensional. The zero mode of the Laplace-Beltrami operator plays a particular role since it is not renormalized at all.
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Güler, Erhan, Hasan Hacısalihoğlu, and Young Kim. "The Gauss Map and the Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space." Symmetry 10, no. 9 (2018): 398. http://dx.doi.org/10.3390/sym10090398.

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We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space E 4 . We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some results. Then, we introduce the third Laplace–Beltrami operator. Moreover, we calculate the third Laplace–Beltrami operator of the rotational hypersurface in E 4 . We also draw some figures of the rotational hypersurface.
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Wang, Ruimin, Zhouwang Yang, Ligang Liu, and Qing Chen. "Discretizing Laplace–Beltrami Operator from Differential Quantities." Communications in Mathematics and Statistics 1, no. 3 (2013): 331–50. http://dx.doi.org/10.1007/s40304-013-0018-2.

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Li, Bo. "The Berezin transform and Laplace–Beltrami operator." Journal of Mathematical Analysis and Applications 327, no. 2 (2007): 1155–66. http://dx.doi.org/10.1016/j.jmaa.2006.04.068.

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Balmaseda, Aitor, Fabio Di Cosmo, and Juan Manuel Pérez-Pardo. "On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits." Symmetry 11, no. 8 (2019): 1047. http://dx.doi.org/10.3390/sym11081047.

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An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group G, criteria for the existence of G-invariant self-adjoint extensions of the Laplace–Beltrami operator over a Riemannian manifold are illustrated and critically revisited. These criteria are employed for characterising self-adjoint extensions of the Laplace–Beltrami operator on an infinite set of intervals, Ω , constituting a quantum circuit, which are invariant under a given action of the group Z . A study of the different unitary representations of the group Z on the space of square integrable functions on Ω is performed and the corresponding Z -invariant self-adjoint extensions of the Laplace–Beltrami operator are introduced. The study and characterisation of the invariance properties allows for the determination of the spectrum and generalised eigenfunctions in particular examples.
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Burago, Dmitri, Sergei Ivanov, and Yaroslav Kurylev. "A graph discretization of the Laplace–Beltrami operator." Journal of Spectral Theory 4, no. 4 (2014): 675–714. http://dx.doi.org/10.4171/jst/83.

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Dissertations / Theses on the topic "Laplace-Beltrami-Operator"

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fr, vodev@math univ-nantes. "Uniform Estimates of the Resolvent of the Laplace--Beltrami Operator on Infinite Volume Riemannian Manifolds with Cusps.II." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1044.ps.

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Hildebrandt, Klaus [Verfasser]. "Discretization and approximation of the shape operator, the Laplace-Beltrami operator, and the Willmore energy of surfaces / Klaus Hildebrandt." Berlin : Freie Universität Berlin, 2013. http://d-nb.info/1031106448/34.

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Thangudu, Kedarnath. "Practicality of Discrete Laplace Operators." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1236615194.

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Pester, Cornelia. "A residual a posteriori error estimator for the eigenvalue problem for the Laplace-Beltrami operator." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601556.

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The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in $\R^3$. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the spherical domains and a carefully chosen finite element discretization allows us to use an approach similar to the one for the two-dimensional case. In order to assure results in the quality of those for plane domains, weighted norms and an adapted Clément-type interpolation operator have to be introduced.
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Caissard, Thomas. "Opérateur de Laplace–Beltrami discret sur les surfaces digitales." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1326/document.

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La problématique centrale de cette thèse est l'élaboration d'un opérateur de Laplace--Beltrami discret sur les surfaces digitales. Ces surfaces proviennent de la théorie de la géométrie discrète, c’est-à-dire la géométrie qui s'intéresse à des sous-ensembles des entiers relatifs. Nous nous plaçons ici dans un cadre théorique où les surfaces digitales sont le résultat d'une approximation, ou processus de discrétisation, d'une surface continue sous-jacente. Cette méthode permet à la fois de prouver des théorèmes de convergence des quantités discrètes vers les quantités continues, mais aussi, par des analyses numériques, de confirmer expérimentalement ces résultats. Pour la discrétisation de l’opérateur, nous faisons face à deux problèmes : d'un côté, notre surface n'est qu'une approximation de la surface continue sous-jacente, et de l'autre côté, l'estimation triviale de quantités géométriques sur la surface digitale ne nous apporte pas en général une bonne estimation de cette quantité. Nous possédons déjà des réponses au second problème : ces dernières années, de nombreux articles se sont attachés à développer des méthodes pour approximer certaines quantités géométriques sur les surfaces digitales (comme par exemple les normales ou bien la courbure), méthodes que nous décrirons dans cette thèse. Ces nouvelles techniques d'approximation nous permettent d'injecter des informations de mesure sur les éléments de notre surface. Nous utilisons donc l'estimation de normales pour répondre au premier problème, qui nous permet en fait d'approximer de façon précise le plan tangent en un point de la surface et, via une méthode d'intégration, palier à des problèmes topologiques liées à la surface discrète. Nous présentons un résultat théorique de convergence du nouvel opérateur discrétisé, puis nous illustrons ensuite ses propriétés à l’aide d’une analyse numérique de l’opérateur. Nous effectuons une comparaison détaillée du nouvel opérateur par rapport à ceux de la littérature adaptés sur les surfaces digitales, ce qui nous permet, au moins pour la convergence, de montrer que seul notre opérateur possède cette propriété. Nous illustrons également l’opérateur via quelques unes de ces applications comme sa décomposition spectrale ou bien encore le flot de courbure moyenne<br>The central issue of this thesis is the development of a discrete Laplace--Beltrami operator on digital surfaces. These surfaces come from the theory of discrete geometry, i.e. geometry that focuses on subsets of relative integers. We place ourselves here in a theoretical framework where digital surfaces are the result of an approximation, or discretization process, of an underlying smooth surface. This method makes it possible both to prove theorems of convergence of discrete quantities towards continuous quantities, but also, through numerical analyses, to experimentally confirm these results. For the discretization of the operator, we face two problems: on the one hand, our surface is only an approximation of the underlying continuous surface, and on the other hand, the trivial estimation of geometric quantities on the digital surface does not generally give us a good estimate of this quantity. We already have answers to the second problem: in recent years, many articles have focused on developing methods to approximate certain geometric quantities on digital surfaces (such as normals or curvature), methods that we will describe in this thesis. These new approximation techniques allow us to inject measurement information into the elements of our surface. We therefore use the estimation of normals to answer the first problem, which in fact allows us to accurately approximate the tangent plane at a point on the surface and, through an integration method, to overcome topological problems related to the discrete surface. We present a theoretical convergence result of the discretized new operator, then we illustrate its properties using a numerical analysis of it. We carry out a detailed comparison of the new operator with those in the literature adapted on digital surfaces, which allows, at least for convergence, to show that only our operator has this property. We also illustrate the operator via some of these applications such as its spectral decomposition or the mean curvature flow
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Fedchenko, Dmitry, and Nikolai Tarkhanov. "A Class of Toeplitz Operators in Several Variables." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6893/.

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We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.
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Santos, Fabiana Alves dos. "Espectro de variedades completas e não-compactas." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25815.

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SANTOS, Fabiana Alves dos. Espectro de variedades completas e não-compactas. 2017. 39 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-13T14:03:43Z No. of bitstreams: 1 2017_tese_fasantos.pdf: 609112 bytes, checksum: 0bbcd05e8e335e0ecb00510e212c4e79 (MD5)<br>Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Estou devolvendo a Tese de FABIANA ALVES DOS SANTOS para que ela corrija alguns itens do trabalho: 1- FICHA CATALOGRÁFICA (refaça a ficha catalográfica colocando seu nome completo) 2- FOLHA DE APROVAÇÃO (substitua a folha de aprovação por uma cópia que não contenha as assinaturas dos membros da banca examinadora, pois, por questões de segurança, não estamos mais publicando os trabalhos com as assinaturas dos membros da banca) 3- ITEM ALEATÓRIO (na página 5, há uma frase aleatória - EBENEZER! - que não se enquadra em nenhum dos itens opcionais de uma Tese. Caso seja uma EPÍGRAFE deve aparecer entre aspas duplas, após à página dos agradecimentos, e com a citação do autor ou fonte de onde foi retirada) 4- TÍTULO DO CAP. 3 (coloque o título do capítulo 3, que aparece no SUMÁRIO e no TÍTULO DO CAPITULO, em letra MAIÚSCULA, NEGRITO e FONTE n 12) Atenciosamente, on 2017-09-13T16:42:12Z (GMT)<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-18T13:52:41Z No. of bitstreams: 1 2017_tese_fasantos.pdf: 12798451 bytes, checksum: 062ab3efa4756ce3a83ed52d9cebcd13 (MD5)<br>Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-09-18T15:16:06Z (GMT) No. of bitstreams: 1 2017_tese_fasantos.pdf: 12798451 bytes, checksum: 062ab3efa4756ce3a83ed52d9cebcd13 (MD5)<br>Made available in DSpace on 2017-09-18T15:16:07Z (GMT). No. of bitstreams: 1 2017_tese_fasantos.pdf: 12798451 bytes, checksum: 062ab3efa4756ce3a83ed52d9cebcd13 (MD5) Previous issue date: 2017-01-20<br>On this work we study the espectrum of Laplace-Beltrami operator on the warped Riemannian manifold Mn = R_r Sn1, whose warping function is smooth, positive, periodic, with period a and satis_es r0 = min r(t) < p n 1a=_. We show that spectrum there no eingevalue, is formed by a union of closed intervals, and, from the peridicity of r, using the classical Hill's Equations Theory, we conclude the existence of gaps.<br>Neste trabalho caracterizamos o espectro do operador de Laplace-Beltrami na variedade warped Mn = R_r Sn1 cuja função warping _e suave, positiva, periódica, de período a, e satisfaz r0 = min r(t) < p n 1a=_. Mostramos que tal espectro não possui autovalores, é escrito como a união de intervalos e, da periodicidade de r, utilizamos a clássica teoria a cerca dos operados de Hill, e concluímos e existência de gaps no espectro de M.
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Meyer, Arnd, and Cornelia Pester. "The Laplace and the linear elasticity problems near polyhedral corners and associated eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601506.

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The solutions to certain elliptic boundary value problems have singularities with a typical structure near polyhedral corners. This structure can be exploited to devise an eigenvalue problem whose solution can be used to quantify the singularities of the given boundary value problem. It is necessary to parametrize a ball centered at the corner. There are different possibilities for a suitable parametrization; from the numerical point of view, spherical coordinates are not necessarily the best choice. This is why we do not specify a parametrization in this paper but present all results in a rather general form. We derive the eigenvalue problems that are associated with the Laplace and the linear elasticity problems and show interesting spectral properties. Finally, we discuss the necessity of widely accepted symmetry properties of the elasticity tensor. We show in an example that some of these properties are not only dispensable, but even invalid, although claimed in many standard books on linear elasticity.
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Bolelli, Maria Virginia. "Diffusion Maps for Dimensionality Reduction." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18246/.

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In this thesis we present the diffusion maps, a framework based on diffusion processes for finding meaningful geometric descriptions of data sets. A diffusion process can be described via an iterative application of the heat kernel which has two main characteristics: it satisfies a Markov semigroup property and its level sets encode all geometric features of the space. This process, well known in regular manifolds, has been extended to general data set by Coifman and Lafon. They define a diffusion kernel starting from the geometric properties of the data and their density properties. This kernel will be a compact operator, and the projection on its eigenvectors at different instant of time, provides a family of embeddings of a dataset into a suitable Euclidean space. The projection on the first eigenvectors, naturally leads to a dimensionality reduction algorithm. Numerical implementation is provided on different data set.
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Boldt, Sebastian. "The height of compact nonsingular Heisenberg-like Nilmanifolds." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/18924.

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Die vorliegende Arbeit beschäftigt sich mit der Höhe (-log Determinante) kompakter nicht-singulärer heisenbergartiger Nilmannigfaltigkeiten. Heisenbergartige Nilmannigfaltigkeiten sind Verallgemeinerungen von Heisenbergmannigfaltigkeiten, d.h., kompakter Quotienten der Heisenberg-Gruppe, ausgestattet mit einer linksinvarianten Metrik. Zunächst werden explizite Formeln für die spektrale Zeta-Funktion und die Höhe bewiesen. Mithilfe dieser Formeln werden im Weiteren mehrere Resultate zur Existenz unterer Schranken/Minima der Höhe auf verschiedenen Moduli bewiesen. Zum Beispiel ist die Höhe stets von unten beschränkt, wenn man nur Metriken vom Heisenberg-Typ und mit Volumen 1 auf einer gegebenen Nilmannigfaltigkeit betrachtet. Im Gegensatz dazu hängt die Existenz unterer Schranken für die Höhe auf dem Modulraum der heisenbergartigen Metriken mit Volumen 1 von der Dimension Modulo 4 der zugrundeliegenden Mannigfaltigkeit ab. Im letzten Abschnitt werden konkrete Minima der Höhe behandelt. Wir zeigen, dass gewisse 3-, 5-, 9- und 25-dimensionale Nilmannigfaltigkeiten vom Heisenberg-Typ lokale Minima sind. Diese stehen in Zusammenhang mit den Minima der Höhe flacher Tori in der jeweiligen Dimension minus 1. Zum Abschluss werden diejenigen linksinvarianten Metriken charakterisiert, an denen die Höhe ein globales Minimum auf einer gegebenen dreidimensionalen Nilmannigfaltigkeit annimmt, indem sie zur Höhe flacher 2-dimensionaler Tori in Bezug gesetzt werden.<br>This thesis deals with the height (-log determinant) of compact nonsingular Heisenberg-like nilmanifolds. Heisenberg-like nilmanifolds are generalisations of Heisenberg manifolds, i.e., compact quotients of the Heisenberg group endowed with a left invariant metric. First, an explicit formula for the spectral zeta-function and the height is proved. By means of these formulas, several results concerning the existence of lower bounds/minima for the height on different moduli are proved. For example, while the height is always bounded from below when one considers only volume normalised Heisenberg-type metrics on a fixed nilmanifold, the existence of lower bounds for the height on the moduli space of volume normalised Heisenberg-like metrics depends on the dimension modulo 4 of the underlying nilmanifold. In the last part, we consider concrete minima of the height on Heisenberg manifolds. We show that certain 3-, 5-, 9- and 25-dimensional Heisenberg-type nilmanifolds are (local) minima for the height. These nilmanifolds are related to the minima of the height of flat tori in dimensions one less. Finally, the left invariant metrics at which the height attains a global minimum on any three-dimensional nilmanifold are characterised by relating them to the height of flat 2-dimensional tori.
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Books on the topic "Laplace-Beltrami-Operator"

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Sogge, Christopher D. Geodesics and the Hadamard parametrix. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0002.

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This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω‎ ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω‎, one can choose a natural local coordinate system y = κ‎(x) vanishing at y0 so that the quadratic form associated with the metric takes a special form. To conclude, the chapter turns to the Hadamard parametrix.
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Book chapters on the topic "Laplace-Beltrami-Operator"

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Fraczek, Markus Szymon. "The Hyperbolic Laplace-Beltrami Operator." In Selberg Zeta Functions and Transfer Operators. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51296-9_6.

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Lazutkin, Vladimir F. "Laplace-Beltrami-Schrödinger Operator and Quasimodes." In KAM Theory and Semiclassical Approximations to Eigenfunctions. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-76247-5_7.

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Faraut, Jacques, Adam Korányi, Guy Roos, Soji Kaneyuki, and Qi-keng Lu. "The Laplace-Beltrami Operator in Various Coordinates." In Analysis and Geometry on Complex Homogeneous Domains. Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1366-6_21.

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Xiong, Yunhui, Guiqing Li, and Guoqiang Han. "Mean Laplace–Beltrami Operator for Quadrilateral Meshes." In Transactions on Edutainment V. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18452-9_15.

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Bonito, Andrea, J. Manuel Cascón, Pedro Morin, and Ricardo H. Nochetto. "AFEM for Geometric PDE: The Laplace-Beltrami Operator." In Analysis and Numerics of Partial Differential Equations. Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2592-9_15.

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Caissard, Thomas, David Coeurjolly, Jacques-Olivier Lachaud, and Tristan Roussillon. "Heat Kernel Laplace-Beltrami Operator on Digital Surfaces." In Discrete Geometry for Computer Imagery. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66272-5_20.

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Tarkhanov, Nikolai. "The Laplace-Beltrami Operator on a Rotationally Symmetric Surface." In Recent Trends in Toeplitz and Pseudodifferential Operators. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0548-9_13.

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Craioveanu, Mircea, Mircea Puta, and Themistocles M. Rassias. "Spectral Properties of the Laplace-Beltrami Operator and Applications." In Old and New Aspects in Spectral Geometry. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-2475-3_3.

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Zhang, Qingqing, and Chunmei Duan. "Discretization of Laplace-Beltrami Operator Based on Cotangent Scheme and Its Applications." In Human Centered Computing. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-37429-7_62.

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Wetzler, Aaron, Yonathan Aflalo, Anastasia Dubrovina, and Ron Kimmel. "The Laplace-Beltrami Operator: A Ubiquitous Tool for Image and Shape Processing." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38294-9_26.

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Conference papers on the topic "Laplace-Beltrami-Operator"

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Afrose, Zinat, and Yuzhong Shen. "Mesh color sharpening using Laplace-Beltrami operator." In 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2014. http://dx.doi.org/10.1109/globalsip.2014.7032277.

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Jian Liang, Rongjie Lai, Tsz Wai Wong, and Hongkai Zhao. "Geometric understanding of point clouds using Laplace-Beltrami operator." In 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2012. http://dx.doi.org/10.1109/cvpr.2012.6247678.

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Ghaderpanah, Mohammadreza, Abdullah Abbas, and A. Ben Hamza. "Entropic hashing of 3D objects using Laplace-Beltrami operator." In 2008 15th IEEE International Conference on Image Processing. IEEE, 2008. http://dx.doi.org/10.1109/icip.2008.4712452.

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Bobenko, Alexander I. "Delaunay triangulations of polyhedral surfaces, a discrete Laplace-Beltrami operator and applications." In the twenty-fourth annual symposium. ACM Press, 2008. http://dx.doi.org/10.1145/1377676.1377677.

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Seo, Seongho, Moo K. Chung, Brian J. Whyms, and Houri K. Vorperian. "Mandible shape modeling using the second eigenfunction of the Laplace-Beltrami operator." In SPIE Medical Imaging, edited by Benoit M. Dawant and David R. Haynor. SPIE, 2011. http://dx.doi.org/10.1117/12.877537.

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Brezov, D. S., C. D. Mladenova, and I. M. Mladenov. "Variations of (pseudo-)rotations and the Laplace-Beltrami operator on homogeneous spaces." In RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4934313.

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Pecha, Marek, Pavla Jirutkova, and Martin Cermak. "Fundamental improvements of the piecewise semi-smooth Laplace-Beltrami operator numerical stability." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992519.

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Xu, Xiaoqi, Nicolas Drougard, and Raphaelle N. Roy. "Dimensionality Reduction via the Laplace-Beltrami Operator: Application to EEG-based BCI." In 2021 10th International IEEE/EMBS Conference on Neural Engineering (NER). IEEE, 2021. http://dx.doi.org/10.1109/ner49283.2021.9441404.

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Lefevre, Julien, David Germanaud, Clara Fischer, Roberto Toro, Denis Riviere, and Olivier Coulon. "Fast surface-based measurements using first eigenfunction of the Laplace-Beltrami Operator: Interest for sulcal description." In 2012 IEEE 9th International Symposium on Biomedical Imaging (ISBI 2012). IEEE, 2012. http://dx.doi.org/10.1109/isbi.2012.6235863.

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Kim, Seung-Goo, Johannes Stelzer, Pierre-Louis Bazin, Adrian Viehweger, and Thomas Knosche. "Group-wise analysis on myelination profiles of cerebral cortex using the second eigenvector of Laplace-Beltrami operator." In 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI 2014). IEEE, 2014. http://dx.doi.org/10.1109/isbi.2014.6868043.

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