Mean curvature type flow with perpendicular Neumann boundary condition inside a convex cone
type: Item
instance of: scholarly article
title: Mean curvature type flow with perpendicular Neumann boundary condition inside a convex cone
zbMATH Open document ID: 1476.53112
DOI: 10.1155/2014/315768
author: Fangcheng Guo
author: Guanghan Li
author: Chuanxi Wu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone. We find that the volume enclosed by the cone and the evolving hypersurface is invariant. By maximal principle, we prove that the solutions of this flow exist for all time and converge to some part of a sphere exponentially as \(t\) tends to infinity.
Mathematics Subject Classification ID: 53E10
zbMATH DE Number: 7022152
zbMATH Keywords: convex cone
zbMATH Keywords: volume
zbMATH Keywords: evolving hypersurface is invariant
zbMATH Keywords: maximum principle
Wikidata QID: Q59038151
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/315768
OpenAlex ID: W2131429477
cites work: A Mean Curvature Type Flow in Space Forms
cites work: Non-parametric mean curvature evolution with boundary conditions
cites work: Convergence of solutions to the mean curvature flow with a Neumann boundary condition
cites work: Regularity estimates for solutions to the mean curvature flow with a Neumann boundary condition
cites work: Mean curvature flow with free boundary on smooth hypersurfaces
cites work: The perpendicular Neumann problem for mean curvature flow with a timelike cone boundary condition
cites work: The constant angle problem for mean curvature flow inside rotational tori
cites work: Motion by volume preserving mean curvature flow near cylinders
cites work: Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle
cites work: Q5688819
cites work: Forced convex mean curvature flow in Euclidean spaces
cites work: Q4783632
cites work: Q4354424
cites work: Mean curvature evolution of entire graphs
cites work: Q3342966
description: scientific article; zbMATH DE number 7022152