CaltechAUTHORS
  A Caltech Library Service

Entire surfaces of constant curvature in Minkowski 3-space

Bonsante, Francesco and Seppi, Andrea and Smillie, Peter (2019) Entire surfaces of constant curvature in Minkowski 3-space. Mathematische Annalen . ISSN 0025-5831. (In Press) http://resolver.caltech.edu/CaltechAUTHORS:20190325-135439657

[img] PDF - In Press Version
Creative Commons Attribution.

1352Kb
[img] PDF - Submitted Version
See Usage Policy.

958Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20190325-135439657

Abstract

This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by properly embedded convex surfaces of constant Gaussian curvature. This is a consequence of our classification of surfaces with bounded prescribed Gaussian curvature, sometimes called the Minkowski problem, for which partial results were obtained by Li, Guan-Jian-Schoen, and Bonsante-Seppi. Some applications to minimal Lagrangian self-maps of the hyperbolic plane are obtained.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00208-019-01820-9DOIArticle
https://rdcu.be/bsMtfPublisherFree ReadCube access
https://arxiv.org/abs/1805.08024arXivDiscussion Paper
ORCID:
AuthorORCID
Bonsante, Francesco0000-0002-8091-5301
Smillie, Peter0000-0001-7316-897X
Additional Information:© 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Received 29 May 2018; First Online: 23 March 2019. We thank Jean-Marc Schlenker for his interest and encouragement throughout. The third author also wishes to thank Shing-Tung Yau for inspiring interest in the problem.
Classification Code:Mathematics Subject Classification: Primary: 53C42; Secondary 35J96; 53B30; 53C50
Record Number:CaltechAUTHORS:20190325-135439657
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190325-135439657
Official Citation:Bonsante, F., Seppi, A. & Smillie, P. Math. Ann. (2019). https://doi.org/10.1007/s00208-019-01820-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94125
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Mar 2019 21:01
Last Modified:25 Mar 2019 21:15

Repository Staff Only: item control page