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Anisotropic and crystalline mean curvature flow of mean-convex sets [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive anisotropic mean curvature.
A. Chambolle, M. Novaga
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Convexity estimates for high codimension mean curvature flow [PDF]
Mathematische Annalen, 2020 We consider the flow by mean curvature of smooth n -dimensional submanifolds of $${\mathbb {R}}^{n+k}$$ R n + k , $$k \ge 2$$ k ≥ 2 , which are compact and quadratically pinched.
Lynch Stephen, H. Nguyen
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Uniformly Compressing Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2018 Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a related geometric flow which is free of these drawbacks.
Wenhui Shi, Dmitry Vorotnikov
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Is mean curvature flow a gradient flow?
, 2023 It is well-known that the mean curvature flow is a formal gradient flow of the perimeter functional. However, by the work of Michor and Mumford [7,8], the formal Riemannian structure that is compatible with the gradient flow structure induces a degenerate metric on the space of hypersurfaces.
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Communications in Contemporary Mathematics, 2019 The skew mean curvature flow (SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study the basic properties of the SMCF and prove the existence of a short-time solution to the initial value problem of the SMCF of compact surfaces in Euclidean space [Formula ...
Song, Chong, Sun, Jun
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A survey on Inverse mean curvature flow in ROSSes
Complex Manifolds, 2017 In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces.
Pipoli Giuseppe
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APPROXIMATION OF THE ANISOTROPIC MEAN CURVATURE FLOW [PDF]
Mathematical Models and Methods in Applied Sciences, 2007 In this paper, we provide simple proofs of consistency for two well-known algorithms for mean curvature motion, Almgren–Taylor–Wang's1 variational approach, and Merriman–Bence–Osher's algorithm.29 Our techniques, based on the same notion of strict sub- and superflows, also work in the (smooth) anisotropic case.
CHAMBOLLE A, NOVAGA, MATTEO
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Mean Convex Mean Curvature Flow with Free Boundary [PDF]
Communications on Pure and Applied Mathematics, 2021 AbstractIn this paper, we generalize White's regularity and structure theory for mean‐convex mean curvature flow [45, 46, 48] to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound
Edelen, Nick +3 more
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A nonlinear partial differential equation for the volume preserving mean curvature flow
Networks and Heterogeneous Media, 2013 We analyze the evolution of multi-dimensional normal graphs overthe unit sphere under volume preserving mean curvature flow andderive a non-linear partial differential equation in polarcoordinates.
Dimitra Antonopoulou, Georgia Karali
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Ancient solutions in Lagrangian mean curvature flow
, 2020 Ancient solutions of Lagrangian mean curvature flow in C^n naturally arise as Type II blow-ups. In this extended note we give structural and classification results for such ancient solutions in terms of their blow-down and, motivated by the Thomas-Yau ...
Lambert, Ben +2 more
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