Limit shape of the cross-section of shrinking doughnuts
type: Item
instance of: scholarly article
title: Limit shape of the cross-section of shrinking doughnuts
zbMATH Open document ID: 0783.53006
author: Naoyuki Ishimura
published in: Journal of the Mathematical Society of Japan
publication date: 1994-03-08T00:00:00Z
review text: We discuss the asymptotic behaviour of symmetric tori which are shrinking to a circle by the mean curvature flow. Employing the backward heat kernel analysis we show that the limit shape of its cross-section is a circle. The assumption we set is that the isoperimetric ratio of the generating curve remains bounded as shrinking, which follows in particular from the convexity of curves.
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 469079
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: singularities
zbMATH Keywords: mean curvature flow
zbMATH Keywords: isoperimetric ratio
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04530569
OpenAlex ID: W2046244520
DOI: 10.2969/JMSJ/04530569
description: scientific article; zbMATH DE number 469079