A remark on soliton equation of mean curvature flow [PDF]
Anais da Academia Brasileira de Ciências, 2004 In this note, we consider self-similar immersions of the mean curvature flow and show that a graph solution of the soliton equation, provided it has bounded derivative, converges smoothly to a function which has some special properties (see Theorem 1.1 ...
Li Ma, Yang Yang
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Conformal solitons for the mean curvature flow in hyperbolic space [PDF]
Annals of Global Analysis and Geometry, 2023 In this paper, we study conformal solitons for the mean curvature flow in hyperbolic space Hn+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
L. Mari +3 more
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Inverse mean curvature flow and Ricci-pinched three-manifolds [PDF]
Journal für die Reine und Angewandte Mathematik, 2023 Let ( M , g ) (M,g) be a noncompact, connected, complete Riemannian three-manifold with nonnegative Ricci curvature satisfying Ric ≥ ε tr ( Ric ) g \mathrm{Ric}\geq\varepsilon\operatorname{tr}(\mathrm{Ric})g for some ε > 0 \varepsilon>0 .
G. Huisken, T. Koerber
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Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces [PDF]
Numerische Mathematik, 2022 An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a ...
C. M. Elliott +2 more
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Weak-strong uniqueness for volume-preserving mean curvature flow [PDF]
Revista matemática iberoamericana, 2022 In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the concept in the ...
Tim Laux
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The Existence of a Weak Solution to Volume Preserving Mean Curvature Flow in Higher Dimensions [PDF]
Archive for Rational Mechanics and Analysis, 2022 In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of $$L^2$$ L 2 -flow.
K. Takasao
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A constrained mean curvature flow and Alexandrov-Fenchel inequalities [PDF]
, 2022 In this article, we study a locally constrained mean curvature flow for star-shaped hypersurfaces with capillary boundary in the half-space. We prove its long-time existence and the global convergence to a spherical cap.
Xinqun Mei, Guofang Wang, Liangjun Weng
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Mean curvature flow with generic low-entropy initial data [PDF]
Duke mathematical journal, 2021 We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem applies to all closed surfaces in $\mathbb{R}^3$ with entropy $\leq 2$ and
Otis Chodosh +3 more
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Noncompact self-shrinkers for mean curvature flow with arbitrary genus [PDF]
Journal für die Reine und Angewandte Mathematik, 2021 In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, we employ min-max techniques to give a rigorous existence proof for these surfaces.
R. Buzano, H. Nguyen, Mario B. Schulz
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Convergence of Dziuk's semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements [PDF]
SIAM Journal on Numerical Analysis, 2021 Dziuk's surface finite element method (FEM) for mean curvature flow has had a significant impact on the development of parametric and evolving surface FEMs for surface evolution equations and curva...
Buyang Li
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