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Weighted Mean Curvature [PDF]

Signal Processing, 2019
In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient ...
Goksel, Orcun, Gong, Yuanhao
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The mean curvature at the first singular time of the mean curvature flow [PDF]

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010
Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. We prove that the
Brakke, Choi, Colding, Colding, Cooper, Ecker, Ecker, Ecker, Huisken, Huisken, Huisken, Huisken, Ilmanen, Ilmanen, Le, Nam Q. Le, Natasa Sesum, Schätzle, Shen, Simon, Smoczyk, Stone, White, White, White, Xu, Xu   +26 more
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Curvature estimates for surfaces with bounded mean curvature [PDF]

Transactions of the American Mathematical Society, 2011
Estimates for the norm of the second fundamental form, $|A|$, play a crucial role in studying the geometry of surfaces. In fact, when $|A|$ is bounded the surface cannot bend too sharply.
Bourni, Theodora, Tinaglia, Giuseppe
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Constant mean curvature surfaces [PDF]

Surveys in Differential Geometry, 2016
In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for $H$-laminations and CMC foliations of Riemannian $n ...
Meeks III, William H., Perez, Joaquin, Tinaglia, Giuseppe   +2 more
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Mean curvature flow with obstacles [PDF]

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2012
We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme.
Almeida, Luís, Chambolle, Antonin, Novaga, Matteo   +2 more
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The hyperbolic mean curvature flow [PDF]

Journal de Mathématiques Pures et Appliquées, 2007
We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector.
LeFloch, Philippe G., Smoczyk, Knut
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Surfaces of constant mean curvature [PDF]

Proceedings of the American Mathematical Society, 1966
Joseph A. Wolf
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How Membrane Geometry Regulates Protein Sorting Independently of Mean Curvature [PDF]

ACS Central Science, 2020
Jannik B. Larsen, Kadla R. Rosholm, Celeste Kennard, Søren L. Pedersen, Henrik K. Munch, Vadym Tkach, John J. Sakon, Thomas Bjørnholm, Keith R. Weninger, Poul Martin Bendix, Knud J. Jensen, Nikos S Hatzakis, Mark J. Uline, Dimitrios Stamou   +13 more
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Weighted Ricci curvature in Riemann-Finsler geometry [PDF]

AUT Journal of Mathematics and Computing, 2021
Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
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Motion by crystalline-like mean curvature: A survey

Bulletin of Mathematical Sciences, 2022
We consider a class of anisotropic curvature flows called crystalline curvature flows. We present a survey on this class of flows with special emphasis on the well-posedness of its initial value problem.
Yoshikazu Giga, Norbert Požár
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