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

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

2 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

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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.",

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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.

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

Abstract

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