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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, 374 (3-4). pp. 1261-1309. ISSN 0025-5831. doi:10.1007/s00208-019-01820-9.

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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 ReadCube access Paper
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 (, 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.
Issue or Number:3-4
Classification Code:Mathematics Subject Classification: Primary: 53C42; Secondary 35J96; 53B30; 53C50
Record Number:CaltechAUTHORS:20190325-135439657
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Official Citation:Bonsante, F., Seppi, A. & Smillie, P. Math. Ann. (2019) 374: 1261.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94125
Deposited By: Tony Diaz
Deposited On:25 Mar 2019 21:01
Last Modified:16 Nov 2021 17:02

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