Classification of noncollapsed translators in ℝ4

Kyeongsu Choi; Robert Haslhofer; Or Hershkovits

doi:10.4310/cjm.2023.v11.n3.a1

Classification of noncollapsed translators in ℝ⁴

Kyeongsu Choi, Robert Haslhofer, Or Hershkovits

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in ℝ⁴ or more generally in 4-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in ℝ⁴ is either ℝ×2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.

Original language	English
Pages (from-to)	563-698
Number of pages	136
Journal	CAMBRIDGE JOURNAL OF MATHEMATICS
Volume	11
Issue number	3
DOIs	https://doi.org/10.4310/cjm.2023.v11.n3.a1
State	Published - 2023

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.4310/cjm.2023.v11.n3.a1

Cite this

@article{ab4f8a324f4e4a6c8e85e6febd5924b3,

title = "Classification of noncollapsed translators in ℝ4",

abstract = "In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in ℝ4 or more generally in 4-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in ℝ4 is either ℝ×2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.",

author = "Kyeongsu Choi and Robert Haslhofer and Or Hershkovits",

year = "2023",

doi = "10.4310/cjm.2023.v11.n3.a1",

language = "الإنجليزيّة",

volume = "11",

pages = "563--698",

journal = "CAMBRIDGE JOURNAL OF MATHEMATICS",

issn = "2168-0930",

publisher = "International Press, Inc.",

number = "3",

}

TY - JOUR

T1 - Classification of noncollapsed translators in ℝ4

AU - Choi, Kyeongsu

AU - Haslhofer, Robert

AU - Hershkovits, Or

PY - 2023

Y1 - 2023

N2 - In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in ℝ4 or more generally in 4-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in ℝ4 is either ℝ×2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.

AB - In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in ℝ4 or more generally in 4-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in ℝ4 is either ℝ×2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.

UR - http://www.scopus.com/inward/record.url?scp=85169926055&partnerID=8YFLogxK

U2 - 10.4310/cjm.2023.v11.n3.a1

DO - 10.4310/cjm.2023.v11.n3.a1

M3 - مقالة

SN - 2168-0930

VL - 11

SP - 563

EP - 698

JO - CAMBRIDGE JOURNAL OF MATHEMATICS

JF - CAMBRIDGE JOURNAL OF MATHEMATICS

IS - 3

ER -

Classification of noncollapsed translators in ℝ⁴

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this