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Mean curvature flow in an extended Ricci flow background [PDF]
, 2023 In this paper, we consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying a mean curvature flow in a Ricci flow background.
Gomes, José N. V., Hudson, Matheus
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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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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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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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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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Lagrangian mean curvature flow with boundary
Calculus of Variations and Partial Differential Equations, 2022 We introduce Lagrangian mean curvature flow with boundary in Calabi--Yau manifolds by defining a natural mixed Dirichlet-Neumann boundary condition, and prove that under this flow, the Lagrangian condition is preserved. We also study in detail the flow of equivariant Lagrangian discs with boundary on the Lawlor neck and the self-shrinking Clifford ...
Evans, CG, Lambert, B, Wood, A
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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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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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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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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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