Mean curvature flow closes open ends of noncompact surfaces of rotation

Yoshikazu Giga, Yukihiro Seki, Noriaki Umeda

研究成果: ジャーナルへの寄稿記事

5 引用 (Scopus)

抄録

We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.

元の言語英語
ページ(範囲)1508-1529
ページ数22
ジャーナルCommunications in Partial Differential Equations
34
発行部数11
DOI
出版物ステータス出版済み - 1 1 2009

Fingerprint

Mean Curvature Flow
Hypersurface
Quenching
Shrinking
Infinity
Tend
Closed
Motion

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

これを引用

Mean curvature flow closes open ends of noncompact surfaces of rotation. / Giga, Yoshikazu; Seki, Yukihiro; Umeda, Noriaki.

:: Communications in Partial Differential Equations, 巻 34, 番号 11, 01.01.2009, p. 1508-1529.

研究成果: ジャーナルへの寄稿記事

Giga, Yoshikazu ; Seki, Yukihiro ; Umeda, Noriaki. / Mean curvature flow closes open ends of noncompact surfaces of rotation. :: Communications in Partial Differential Equations. 2009 ; 巻 34, 番号 11. pp. 1508-1529.
@article{b45b0008dcb34c2591cf5e1f15c18cb6,
title = "Mean curvature flow closes open ends of noncompact surfaces of rotation",
abstract = "We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.",
author = "Yoshikazu Giga and Yukihiro Seki and Noriaki Umeda",
year = "2009",
month = "1",
day = "1",
doi = "10.1080/03605300903296926",
language = "English",
volume = "34",
pages = "1508--1529",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",
number = "11",

}

TY - JOUR

T1 - Mean curvature flow closes open ends of noncompact surfaces of rotation

AU - Giga, Yoshikazu

AU - Seki, Yukihiro

AU - Umeda, Noriaki

PY - 2009/1/1

Y1 - 2009/1/1

N2 - We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.

AB - We discuss the motion of noncompact axisymmetric hypersurfaces Γt evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.

UR - http://www.scopus.com/inward/record.url?scp=74949083849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74949083849&partnerID=8YFLogxK

U2 - 10.1080/03605300903296926

DO - 10.1080/03605300903296926

M3 - Article

AN - SCOPUS:74949083849

VL - 34

SP - 1508

EP - 1529

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 11

ER -