Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions

The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in [Formula: see text] (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 equ...

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Autores principales: Huang, Jiaxi, Tataru, Daniel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8844252/
https://www.ncbi.nlm.nih.gov/pubmed/35221347
http://dx.doi.org/10.1007/s00220-021-04303-8
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author Huang, Jiaxi
Tataru, Daniel
author_facet Huang, Jiaxi
Tataru, Daniel
author_sort Huang, Jiaxi
collection PubMed
description The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in [Formula: see text] (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 [Formula: see text] .
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spelling pubmed-88442522022-02-23 Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions Huang, Jiaxi Tataru, Daniel Commun Math Phys Article The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in [Formula: see text] (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 [Formula: see text] . Springer Berlin Heidelberg 2022-01-15 2022 /pmc/articles/PMC8844252/ /pubmed/35221347 http://dx.doi.org/10.1007/s00220-021-04303-8 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Huang, Jiaxi
Tataru, Daniel
Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions
title Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions
title_full Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions
title_fullStr Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions
title_full_unstemmed Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions
title_short Local Well-Posedness of Skew Mean Curvature Flow for Small Data in [Formula: see text] Dimensions
title_sort local well-posedness of skew mean curvature flow for small data in [formula: see text] dimensions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8844252/
https://www.ncbi.nlm.nih.gov/pubmed/35221347
http://dx.doi.org/10.1007/s00220-021-04303-8
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