Embeddedness of timelike maximal surfaces in (1+2)-Minkowski Space

Journal article

Abstract:: We prove that if ϕ: R2→ R1 + 2 is a smooth, proper, timelike immersion with vanishing mean curvature, then necessarily ϕ is an embedding, and every compact subset of ϕ(R2) is a smooth graph. It follows that if one evolves any smooth, self-intersecting spacelike curve (or any planar spacelike curve whose unit tangent vector spans a closed semi-circle) so as to trace a timelike surface of vanishing mean curvature in R1 + 2, then the evolving surface will either fail to ...
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Institution:

University of Oxford

Division:

MPLS

Department:

Physics

Role:

Author

Copyright holder:: Adam Paxton.
Notes:: 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. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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