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

^*Corresponding author for this work

School of Mathematics and Statistics

Ningbo University
University of California at Berkeley

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

Abstract

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].

Original language	English
Pages (from-to)	3748-3798
Number of pages	51
Journal	International Mathematics Research Notices
Volume	2024
Issue number	5
DOIs	https://doi.org/10.1093/imrn/rnad104
Publication status	Published - 1 Mar 2024

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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].",

author = "Jiaxi Huang and Ze Li and Daniel Tataru",

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N2 - 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].

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].

UR - https://www.scopus.com/pages/publications/85187348569

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JO - International Mathematics Research Notices

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

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