Results 21 to 30 of about 43,149 (167)
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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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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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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Diameter Estimate in Geometric Flows
Mathematics, 2023 We prove the upper and lower bounds of the diameter of a compact manifold (M,g(t)) with dimRM=n(n≥3) and a family of Riemannian metrics g(t) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow,
Shouwen Fang, Tao Zheng
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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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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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Mathematical and Computational Applications, 2019 We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was ...
Miyuki Koiso
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Graphical translators for mean curvature flow [PDF]
Calculus of Variations and Partial Differential Equations, 2019 In the published version of the article, there was an incorrect reference, and, consequently, a correction appeared in a subsequent issue of the journal.
Hoffman, D. +3 more
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Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone
Abstract and Applied Analysis, 2014 We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone.
Fangcheng Guo, Guanghan Li, Chuanxi Wu
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