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^*

^*此作品的通讯作者

Peking University
University of California at Berkeley

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1569-1645
页数	77
期刊	Communications in Mathematical Physics
卷	389
期	3
DOI	https://doi.org/10.1007/s00220-021-04303-8
出版状态	已出版 - 2月 2022
已对外发布	是

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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.",

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

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