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Relevant bibliographies by topics / Mean curvature of geodesic spheres

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Academic literature on the topic 'Mean curvature of geodesic spheres'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Mean curvature of geodesic spheres"

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BESSA, G. P., and J. F. MONTENEGRO. "On Cheng's eigenvalue comparison theorem." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (2008): 673–82. http://dx.doi.org/10.1017/s0305004107000965.

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AbstractWe observe that Cheng's Eigenvalue Comparison Theorem for normal geodesic balls [4] is still valid if we impose bounds on the mean curvature of the distance spheres instead of bounds on the sectional and Ricci curvatures. In this version, there is a weak form of rigidity in case of equality of the eigenvalues. Namely, equality of the eigenvalues implies that the distance spheres of the same radius on each ball has the same mean curvature. On the other hand, we construct smooth metrics $g_{\kappa}$ on $[0,r]\times \mathbb{S}^{3}$, non-isometric to the standard metric canκ of constant se

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ROTH, JULIEN, and ABHITOSH UPADHYAY. "ON ALMOST STABLE CMC HYPERSURFACES IN MANIFOLDS OF BOUNDED SECTIONAL CURVATURE." Bulletin of the Australian Mathematical Society 101, no. 2 (2019): 333–38. http://dx.doi.org/10.1017/s0004972719000935.

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Huckemann, Stephan, and Herbert Ziezold. "Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces." Advances in Applied Probability 38, no. 02 (2006): 299–319. http://dx.doi.org/10.1017/s0001867800000987.

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Classical principal component analysis on manifolds, for example on Kendall's shape spaces, is carried out in the tangent space of a Euclidean mean equipped with a Euclidean metric. We propose a method of principal component analysis for Riemannian manifolds based on geodesics of the intrinsic metric, and provide a numerical implementation in the case of spheres. This method allows us, for example, to compare principal component geodesics of different data samples. In order to determine principal component geodesics, we show that in general, owing to curvature, the principal component geodesic

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Huckemann, Stephan, and Herbert Ziezold. "Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces." Advances in Applied Probability 38, no. 2 (2006): 299–319. http://dx.doi.org/10.1239/aap/1151337073.

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Classical principal component analysis on manifolds, for example on Kendall's shape spaces, is carried out in the tangent space of a Euclidean mean equipped with a Euclidean metric. We propose a method of principal component analysis for Riemannian manifolds based on geodesics of the intrinsic metric, and provide a numerical implementation in the case of spheres. This method allows us, for example, to compare principal component geodesics of different data samples. In order to determine principal component geodesics, we show that in general, owing to curvature, the principal component geodesic

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Cheng, Qing-Ming, Haizhong Li, and Guoxin Wei. "The stability index of hypersurfaces with constant scalar curvature in spheres." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 3 (2014): 447–53. http://dx.doi.org/10.1017/s030821051200056x.

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The totally umbilical and non-totally geodesic hypersurfaces in the (n + 1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. In our 2010 paper we proved that the weak stability index of a compact hypersurface M with constant scalar curvature n(n − 1)r, r> 1, in an (n + 1)-dimensional sphere Sn + 1(1), which is not a totally umbilical hypersurface, is greater than or equal to n + 2 if the mean curvature H and H3 are constant. In this paper, we prove the same results, without the assumption that H3 is constant. In fact, we show that the weak stabili

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Li, Haizhong, Yong Wei, and Changwei Xiong. "A note on Weingarten hypersurfaces in the warped product manifold." International Journal of Mathematics 25, no. 14 (2014): 1450121. http://dx.doi.org/10.1142/s0129167x14501213.

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In this paper, we consider the closed embedded hypersurface Σ in the warped product manifold [Formula: see text] equipped with the metric g = dr2 + λ(r)2 gN. We give some characterizations of slice {r} × N by the condition that Σ has constant weighted higher-order mean curvatures (λ′)αpk, or constant weighted higher-order mean curvature ratio (λ′)αpk/p1, which generalize Brendle's [Constant mean curvature surfaces in warped product manifolds, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 247–269] and Brendle–Eichmair's [Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J.

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Roth, Julien. "New stability results for spheres and Wulff shapes." Communications in Mathematics 26, no. 2 (2018): 153–67. http://dx.doi.org/10.2478/cm-2018-0012.

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AbstractWe prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp-sense is W2,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].

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Sheng, Weimin, and Haobin Yu. "Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow." Communications in Contemporary Mathematics 19, no. 01 (2016): 1550092. http://dx.doi.org/10.1142/s0219199715500923.

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We consider the problem of deforming a one-parameter family of hypersurfaces immersed into closed Riemannian manifolds with positive curvature operator. The hypersurface in this family satisfies mean curvature flow while the ambient metric satisfying the normalized Ricci flow. We prove that if the initial background manifold is an approximation of a spherical space form and the initial hypersurface also satisfies a suitable pinching condition, then either the hypersurfaces shrink to a round point in finite time or converge to a totally geodesic sphere as the time tends to infinity.

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Mendonça, Bruno, and Ruy Tojeiro. "Umbilical Submanifolds of Sn × R." Canadian Journal of Mathematics 66, no. 2 (2014): 400–428. http://dx.doi.org/10.4153/cjm-2013-003-3.

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AbstractWe give a complete classification of umbilical submanifolds of arbitrary dimension and codimension of ×ℝ, extending the classification of umbilical surfaces in ×ℝ by Souam and Toubiana as well as the local description of umbilical hypersurfaces in × ℝ by Van der Veken and Vrancken. We prove that, besides small spheres in a slice, up to isometries of the ambient space they come in a two-parameter family of rotational submanifolds whose substantial codimension is either one or two and whose profile is a curve in a totally geodesic ×ℝ or ×ℝ, respectively, the former case arising in a one-

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Alías, Luis J. "An integral formula for compact hypersurfaces in space forms and its applications." Journal of the Australian Mathematical Society 74, no. 2 (2003): 239–48. http://dx.doi.org/10.1017/s144678870000327x.

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AbstractIn this paper we establish an integral formula for compact hypersurfaces in non-flat space forms, and apply it to derive some interesting applications. In particular, we obtain a characterization of geodesic spheres in terms of a relationship between the scalar curvature of the hypersurface and the size of its Gauss map image. We also derive an inequality involving the average scalar curvature of the hypersurface and the radius of a geodesic ball in the ambient space containing the hypersurface, characterizing the geodesic spheres as those for which equality holds.

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Dissertations / Theses on the topic "Mean curvature of geodesic spheres"

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Pinto, Victor Gomes. "Caracterizações da esfera em formas espaciais." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/24227.

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PINTO, V. G. Caracterizações da esfera em formas espaciais. 2017. 79 f. Dissertação (Mestrado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-07-20T20:40:07Z No. of bitstreams: 1 2017_dis_vgpinto.pdf: 1180135 bytes, checksum: f3aa196ed8b0d38c5a2a33642fdb7d0b (MD5)<br>Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia Andrea, Favor informar ao aluno os motivos da rejeição. Faltou a conclusão (item obrigatório) E as referências não estão normalizadas. Seguem os modelos ARTIGOS DE PERIÓDIC

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Monte, Luiz AntÃnio Caetano. "Espectro essencial de uma classe de variedades riemannianas." Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=9185.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico<br>CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Neste trabalho, provaremos alguns resultados sobre espectro essencial de uma classe de variedades Riemannianas, nÃo necessariamente completas, com condiÃÃes de curvatura na vizinhanÃa de um raio. Sobre essas condiÃÃes obtemos que o espectro essencial do operador de Laplace contÃm um intervalo. Como aplicaÃÃo, obteremos o espectro do operador de Laplace de regiÃes ilimitadas dos espaÃos formas, tais como a horobola do espaÃo hiperbÃlico e cones do espaÃo Euclidiano. Co

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Shiau, Shenq-Jong, and 蕭勝中. "Spheres with Prescribed Mean Curvature." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/24417793697519652979.

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碩士<br>國立交通大學<br>應用數學系<br>86<br>In this paper we establish the existence of an embedding Y:Sn→ Sn+1 with the prescribed mean curvature H. In the case of Y is a graph on Sn, this problem is a quasilinear elliptic equation on the sphere Sn. The key to our study of this equation is the Schauder-type estimates. Under certain conditions on H, we find a maximum estimate and a gradient estimate. Based on the continulity method, we obtain the result of existence.

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Book chapters on the topic "Mean curvature of geodesic spheres"

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Alencar, Hilário, and Manfredo do Carmo. "Hypersurfaces With Constant Mean Curvature in Spheres." In Manfredo P. do Carmo – Selected Papers. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25588-5_25.

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