Ancient solutions of the mean curvature flow

Robert Haslhofer; Or Hershkovits

doi:10.4310/CAG.2016.v24.n3.a6

Ancient solutions of the mean curvature flow

Research output: Contribution to journal › Article › peer-review

Abstract

In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t ⇒ 0 collapse to a round point, but for t⇒ - ∞ become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders S^j × ℝ^n-j and near the tips they have asymptotic translators modeled on Bowl^j+1 × ℝ^n-j-1. We also obtain a characterization of the round shrinking sphere among ancient α-Andrews flows, and logarithmic asymptotics.

Original language	English
Pages (from-to)	593-604
Number of pages	12
Journal	Communications in Analysis and Geometry
Volume	24
Issue number	3
DOIs	https://doi.org/10.4310/CAG.2016.v24.n3.a6
State	Published - 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

Access to Document

10.4310/CAG.2016.v24.n3.a6

Cite this

@article{1505e196dd63472d8ade04d895e6f8f1,

title = "Ancient solutions of the mean curvature flow",

abstract = "In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t ⇒ 0 collapse to a round point, but for t⇒ - ∞ become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders Sj × ℝn-j and near the tips they have asymptotic translators modeled on Bowlj+1 × ℝn-j-1. We also obtain a characterization of the round shrinking sphere among ancient α-Andrews flows, and logarithmic asymptotics.",

author = "Robert Haslhofer and Or Hershkovits",

year = "2016",

doi = "10.4310/CAG.2016.v24.n3.a6",

language = "الإنجليزيّة",

volume = "24",

pages = "593--604",

journal = "Communications in Analysis and Geometry",

issn = "1019-8385",

publisher = "International Press of Boston, Inc.",

number = "3",

}

TY - JOUR

T1 - Ancient solutions of the mean curvature flow

AU - Haslhofer, Robert

AU - Hershkovits, Or

PY - 2016

Y1 - 2016

N2 - In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t ⇒ 0 collapse to a round point, but for t⇒ - ∞ become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders Sj × ℝn-j and near the tips they have asymptotic translators modeled on Bowlj+1 × ℝn-j-1. We also obtain a characterization of the round shrinking sphere among ancient α-Andrews flows, and logarithmic asymptotics.

AB - In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t ⇒ 0 collapse to a round point, but for t⇒ - ∞ become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders Sj × ℝn-j and near the tips they have asymptotic translators modeled on Bowlj+1 × ℝn-j-1. We also obtain a characterization of the round shrinking sphere among ancient α-Andrews flows, and logarithmic asymptotics.

UR - http://www.scopus.com/inward/record.url?scp=84976332645&partnerID=8YFLogxK

U2 - 10.4310/CAG.2016.v24.n3.a6

DO - 10.4310/CAG.2016.v24.n3.a6

M3 - مقالة

SN - 1019-8385

VL - 24

SP - 593

EP - 604

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 3

ER -

Ancient solutions of the mean curvature flow

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this