Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d≥ 4 Dimensions

Jiaxi Huang; Daniel Tataru

doi:10.1007/s00220-021-04303-8

Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d≥ 4 Dimensions

Jiaxi Huang
, Daniel Tataru^*

^*Corresponding author for this work

Peking University
Department of Mathematics
University of California at Berkeley

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

3 Citations (Scopus)

Abstract

The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in R^d⁺² (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 4.

Original language	English
Pages (from-to)	1569-1645
Number of pages	77
Journal	Communications in Mathematical Physics
Volume	389
Issue number	3
DOIs	https://doi.org/10.1007/s00220-021-04303-8
Publication status	Published - Feb 2022
Externally published	Yes

Access to Document

10.1007/s00220-021-04303-8

Cite this

@article{23b9b0143ee14a3f81fd668eacdb1a68,

title = "Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d≥ 4 Dimensions",

abstract = "The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (or more generally, in a Riemannian manifold). It can be viewed as a Schr{\"o}dinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schr{\"o}dinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 4.",

author = "Jiaxi Huang and Daniel Tataru",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = feb,

doi = "10.1007/s00220-021-04303-8",

language = "English",

volume = "389",

pages = "1569--1645",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d≥ 4 Dimensions

AU - Huang, Jiaxi

AU - Tataru, Daniel

PY - 2022/2

Y1 - 2022/2

N2 - The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 4.

AB - The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in Rd+2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension d≥ 4.

UR - https://www.scopus.com/pages/publications/85123063206

U2 - 10.1007/s00220-021-04303-8

DO - 10.1007/s00220-021-04303-8

M3 - Article

AN - SCOPUS:85123063206

SN - 0010-3616

VL - 389

SP - 1569

EP - 1645

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d≥ 4 Dimensions

Abstract

Access to Document

Other files and links

Fingerprint

Cite this