Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥4 Dimensions

Jiaxi Huang; Ze Li; Daniel Tataru

doi:10.1093/imrn/rnad104

Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥4 Dimensions

Jiaxi Huang
, Ze Li^*
, Daniel Tataru

^*此作品的通讯作者

数学学院

Ningbo University
University of California at Berkeley

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

The skew mean curvature fow is an evolution equation for a d dimensional manifold immersed into R^d+ ², and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature fow in dimensions d 4. This extends the local well-posedness result in [7].

源语言	英语
页（从-至）	3748-3798
页数	51
期刊	International Mathematics Research Notices
卷	2024
期	5
DOI	https://doi.org/10.1093/imrn/rnad104
出版状态	已出版 - 1 3月 2024

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10.1093/imrn/rnad104

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title = "Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥4 Dimensions",

abstract = "The skew mean curvature fow is an evolution equation for a d dimensional manifold immersed into Rd+ 2, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature fow in dimensions d 4. This extends the local well-posedness result in [7].",

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AB - The skew mean curvature fow is an evolution equation for a d dimensional manifold immersed into Rd+ 2, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature fow in dimensions d 4. This extends the local well-posedness result in [7].

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Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥4 Dimensions

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