Vol. 276, No. 2, 2015

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ISSN: 0030-8730
Isometric embedding of negatively curved complete surfaces in Lorentz–Minkowski space

Bing-Long Chen and Le Yin

Vol. 276 (2015), No. 2, 347–367
Abstract

The Hilbert–Efimov theorem states that any complete surface with curvature bounded above by a negative constant cannot be isometrically embedded in 3. We demonstrate that any simply connected smooth complete surface with curvature bounded above by a negative constant admits a smooth isometric embedding into the Lorentz–Minkowski space 2,1.

Keywords
isometric embedding, Hilbert–Efimov theorem, Lorentz–Minkowski space
Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 35J96
Milestones
Received: 28 August 2014
Accepted: 5 January 2015
Published: 15 July 2015
Authors
Bing-Long Chen
Department of Mathematics
Sun Yat-sen University
Guangzhou, 510275
China
Le Yin
College of Mathematics and Computational Science
Shenzhen University
Shenzhen, 518060
China