Collapsing ancient solutions of mean curvature flow

Theodora Bourni; Mat Langford; Giuseppe Tinaglia

doi:10.4310/jdg/1632506300

Collapsing ancient solutions of mean curvature flow

Theodora Bourni, Mat Langford, Giuseppe Tinaglia

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

6 Citations (Scopus)

Abstract

We construct a compact, convex ancient solution of mean curvature flow in ℝⁿ⁺¹ with O(1)×O(n) symmetry that lies in a slab of width π. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, O(n)-invariant ancient solution that lies in a slab of width π and in no smaller slab.

Original language	English
Pages (from-to)	187-219
Number of pages	33
Journal	JOURNAL OF DIFFERENTIAL GEOMETRY
Volume	119
Issue number	2
DOIs	https://doi.org/10.4310/jdg/1632506300
Publication status	Published - Oct 2021

Access to Document

10.4310/jdg/1632506300

Cite this

@article{d9d1bf1191774bd8adbc49206b60cda4,

title = "Collapsing ancient solutions of mean curvature flow",

abstract = "We construct a compact, convex ancient solution of mean curvature flow in ℝn+1 with O(1)×O(n) symmetry that lies in a slab of width π. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, O(n)-invariant ancient solution that lies in a slab of width π and in no smaller slab.",

author = "Theodora Bourni and Mat Langford and Giuseppe Tinaglia",

note = "Funding Information: ∗The second author was partially supported by an Alexander von Humboldt fellowship. †The third author was partially supported by EPSRC grant no. EP/M024512/1. Received May 2, 2018. Publisher Copyright: {\textcopyright} 2021 International Press of Boston, Inc.. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = oct,

doi = "10.4310/jdg/1632506300",

language = "English",

volume = "119",

pages = "187--219",

journal = "JOURNAL OF DIFFERENTIAL GEOMETRY",

issn = "0022-040X",

publisher = "International Press",

number = "2",

}

TY - JOUR

T1 - Collapsing ancient solutions of mean curvature flow

AU - Bourni, Theodora

AU - Langford, Mat

AU - Tinaglia, Giuseppe

N1 - Funding Information: ∗The second author was partially supported by an Alexander von Humboldt fellowship. †The third author was partially supported by EPSRC grant no. EP/M024512/1. Received May 2, 2018. Publisher Copyright: © 2021 International Press of Boston, Inc.. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/10

Y1 - 2021/10

N2 - We construct a compact, convex ancient solution of mean curvature flow in ℝn+1 with O(1)×O(n) symmetry that lies in a slab of width π. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, O(n)-invariant ancient solution that lies in a slab of width π and in no smaller slab.

AB - We construct a compact, convex ancient solution of mean curvature flow in ℝn+1 with O(1)×O(n) symmetry that lies in a slab of width π. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, O(n)-invariant ancient solution that lies in a slab of width π and in no smaller slab.

UR - http://www.scopus.com/inward/record.url?scp=85115955563&partnerID=8YFLogxK

U2 - 10.4310/jdg/1632506300

DO - 10.4310/jdg/1632506300

M3 - Article

AN - SCOPUS:85115955563

SN - 0022-040X

VL - 119

SP - 187

EP - 219

JO - JOURNAL OF DIFFERENTIAL GEOMETRY

JF - JOURNAL OF DIFFERENTIAL GEOMETRY

IS - 2

ER -

Collapsing ancient solutions of mean curvature flow

Abstract

Access to Document

Other files and links

Fingerprint

Cite this