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The volume preserving mean curvature flow. [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 1987 Let \(F: M^ n\to {\mathbb{R}}^{n+1}\) be the immersion of a uniformly convex closed hypersurface in \({\mathbb{R}}^{n+1}\). \(M^ n\) is deformed by the evolution equation \(\partial F/\partial t=(h-H)\cdot \nu\) where \(\nu\) is the outer unit normal to M, H is the mean curvature and h is the average of H.
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Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
Abstract and Applied Analysis, 2014 Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-f defined on a domain Ω⊂Rn; then the graph M∇f of ∇f is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space Rn2n with the indefinite metric ...
Ruiwei Xu, Linfen Cao
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Local Capillary Pressure Estimation Based on Curvature of the Fluid Interface – Validation with Two-Phase Direct Numerical Simulations [PDF]
E3S Web of Conferences, 2020 With the advancement of high-resolution three-dimensional X-ray imaging, it is now possible to directly calculate the curvature of the interface of two phases extracted from segmented CT images during two-phase flow experiments to derive capillary ...
Akai Takashi +2 more
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Mean curvature flow of spacelike graphs [PDF]
Mathematische Zeitschrift, 2010 version 5: Math.Z (online first 30 July 2010). version 4: 30 pages: we replace the condition $K_1\geq 0$ by the the weaker one $Ricci_1\geq 0$. The proofs are essentially the same. We change the title to a shorter one.
Li, Guanghan, Salavessa, Isabel M. C.
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Hyperbolic inverse mean curvature flow [PDF]
Czechoslovak Mathematical Journal, 2019 In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$ ($n\geqslant2$) is mean convex and star-shaped.
Mao, Jing, Wu, Chuan-Xi, Zhou, Zhe
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Inverse Mean Curvature Flow With Singularities
International Mathematics Research Notices, 2022 Abstract This paper concerns the inverse mean curvature flow (IMCF) running from the boundary of a convex body that has no regularity assumption. We study the evolution of singularities by looking at the blow-up tangent cone around each singular point.
Choi, Beomjun, Hung, Pei-Ken
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A Comparison Principle for the Mean Curvature Flow Equation with Discontinuous Coefficients
International Journal of Differential Equations, 2016 We study the level set equation in a bounded domain when the velocity of the interface is given by the mean curvature plus a discontinuous velocity. We prove a comparison principle for the initial-boundary value problem whose consequence is uniqueness of
Cecilia De Zan, Pierpaolo Soravia
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Some Characterizations of Generalized Null Scrolls
Mathematics, 2019 In this work, a family of ruled surfaces named generalized null scrolls in Minkowski 3-space are investigated via the defined structure functions. The relations between the base curve and the ruling flow of the generalized null scroll are revealed.
Jinhua Qian +2 more
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A convergent algorithm for forced mean curvature flow driven by diffusion on the surface
Interfaces and free boundaries (Print), 2020 The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction–diffusion process on the surface is formulated as a system that couples the velocity law not only to the surface partial differential equation but also to
Balázs Kovács, Buyang Li, C. Lubich
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Uniqueness of two-convex closed ancient solutions to the mean curvature flow [PDF]
Annals of Mathematics, 2018 In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow ($n \ge 2$) which are uniformly two-convex. We prove that any two such ancient solutions are the same up to translations and scaling.
S. Angenent +2 more
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