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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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Diameter, area, and mean curvature
Differential Geometry and its Applications11 pages, 1 figure.
Chambers, Gregory R., Marx-Kuo, Jared
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Hyperbolic mean curvature flow [PDF]
Journal of Differential Equations, 2009 In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive
He, Chun-Lei, Kong, De-Xing, Liu, Kefeng
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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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How Membrane Geometry Regulates Protein Sorting Independently of Mean Curvature [PDF]
ACS Central Science, 2020 Jannik B. Larsen +13 more
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Spectral Prescribed Mean Curvature [PDF]
CoRRWe consider prescribed mean curvature equations whose solutions are minimal surfaces, constant mean curvature surfaces, or capillary surfaces. We consider both Dirichlet boundary conditions for Plateau problems and nonlinear Neumann boundary conditions for capillary problems and we consider domains in $\mathbf{R}^2$ to be rectangles, disks, or annuli.
Jonas Haug, Rachel Jewell, Ray Treinen
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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 computation scheme for its discretization in practical image processing applications.
Yuanhao Gong, Orcun Goksel
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Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$
Universal Journal of Mathematics and Applications, 2023 In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition $\Delta x_{i}=\lambda _{i}x_{i}$ where $\Delta $ denotes the Laplace operator with respect to the first fundamental form.
Tuğçe Dirim, Betül Bulca Sokur
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Approximations of the mean curvature, and the Buet-Rumpf approximate mean curvature flow
CoRRThe aim of this paper is to generalize the work of B. Buet and M. Rumpf on some definition of the approximate mean curvature vector for varifolds, and its associated mean curvature motions for points clouds. We propose a generalization of the definition of the approximate mean curvature vector in two terms: in terms of linear operators and in terms of ...
Sagueni, Abdelmouksit
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Mean Curvature Dictates the Diffusion of Lipids Along Curved Membranes [PDF]
, 2023 Curved cellular membranes are both abundant and functionally relevant. While novel tomography approaches reveal the structural details of curved membranes, their dynamics pose an experimental challenge.
Balázs, Fábián, Matti, Javanainen
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