Results 21 to 30 of about 134 (57)

Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow

European Journal of Applied Mathematics
The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative ...
Tim Laux, Kerrek Stinson, Clemens Ullrich   +2 more
doaj   +1 more source

Closed self-similar solutions to flows by negative powers of curvature

, 2023
In some warped product manifolds including space forms, we consider closed self-similar solutions to curvature flows whose speeds are negative powers of mean curvature, Gauss curvature and other curvature functions with suitable properties. We prove such
Gao, Shanze
core  

Self-similar solutions to the mean curvature flow in $\mathbb{R}^{3}$

, 2020
In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in $\mathbb{R}^{3}$.
Leandro, Benedito, Novais, Rafael, Reis, Hiuri F. S. dos   +2 more
core  

Quantitative convergence of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow

, 2023
We prove a quantitative convergence result of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow. The proof uses gradient flow calibrations and the relative entropy method, which has been used in the recent literature to prove ...
Kroemer, Milan, Laux, Tim
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Translators invariant under hyperpolar actions

, 2023
In this paper, we consider translators (for the mean curvature flow) given by a graph of a function on a symmetric space $G/K$ of compact type which is invariant under a hyperpolar action on $G/K$.
Fujii, Tomoki, Koike, Naoyuki
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Convergence rate of the weighted conformal mean curvature flow

Analysis and Geometry in Metric Spaces
In this article, we study the convergence rate of the following Yamabe-type flow Rϕ(t)m=0inMand∂∂tg(t)=2(hϕ(t)m−Hϕ(t)m)g(t)∂∂tϕ(t)=m(Hϕ(t)m−hϕ(t)m)on∂M{R}_{\phi \left(t)}^{m}=0\hspace{0.33em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}M\hspace ...
Hamanaka Shota, Tung Ho Pak
doaj   +1 more source

A Mean Curvature Flow Propagating in a Cylinder at Exponential Speed

, 2023
In this paper, we study the long time behaviour of mean curvature flow in a cylinder with Robin boundary conditions. Such a boundary condition can force the solution to have a singular behaviour at the boundary when $t\to \infty$.
Lou, Bendong, Wang, Xiaoliu, Yuan, Lixia
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Approximation of multiphase mean curvature flows with arbitrary nonnegative mobilities

, 2022
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities.
Bonnetier, Eric, Bretin, Elie, Masnou, Simon   +2 more
core   +2 more sources

Graphical mean curvature flow with bounded bi-Ricci curvature

, 2022
We consider the graphical mean curvature flow of strictly area decreasing maps $f:M\to N$, where $M$ is a compact Riemannian manifold of dimension $m>1$ and $N$ a complete Riemannian surface of bounded geometry.
Assimos, Renan, Savas-Halilaj, Andreas, Smoczyk, Knut   +2 more
core   +1 more source

Singularities of low entropy high codimension curve shortening flow

, 2023
We consider curve shortening flow of arbitrary codimension in an Euclidean background. We show that, close to a singularity, the flow is asymptotically planar, paralleling Altschuler's work in the case of space curves, and analyse the blow-up limits of ...
Litzinger, Florian
core