The structure of translating surfaces with finite total curvature

Journal article

Abstract:: In this paper, we prove that any mean curvature flow translator Σ² ⊂ R³ with finite total curvature and one end must be a plane. We also prove that if the translator Σ has multiple ends, they are asymptotic to a plane Π containing the direction of translation and can be written as graphs over Π. Finally, we determine that the ends of Σ are strongly asymptotic to Π and obtain quantitative estimates for their asymptotic behavior.

Files:: Khan_2023_The_structure_of.pdf

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Publisher:: Springer
Journal:: Calculus of Variations and Partial Differential Equations More from this journal
Volume:: 62
Issue:: 3
Article number:: 104
Publication date:: 2023-02-24
Acceptance date:: 2023-01-04
DOI:: 10.1007/s00526-023-02441-6
EISSN:: 1432-0835
ISSN:: 0944-2669

Copyright holder:: Khan
Rights statement:: © The Author(s) 2023. Open Access. This 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.

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