Journal article
Embeddedness of timelike maximal surfaces in (1+2)-Minkowski Space
- 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 remain timelike, or it will fail to remain smooth. We show that, even allowing for null points, such a Cauchy evolution will be C2 inextendible beyond some singular time. In addition we study the continuity of the unit tangent for the evolution of a self-intersecting curve in isothermal gauge, which defines a well-known evolution beyond singular time.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1007/s00023-020-00939-9
Authors
- Publisher:
- Springer
- Journal:
- Annales Henri Poincaré More from this journal
- Volume:
- 21
- Issue:
- 9
- Pages:
- 3035–3068
- Publication date:
- 2020-07-24
- Acceptance date:
- 2020-07-10
- DOI:
- EISSN:
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1424-0661
- ISSN:
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1424-0637
- Language:
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English
- Keywords:
- Pubs id:
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1126412
- Local pid:
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pubs:1126412
- Deposit date:
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2020-10-01
- ARK identifier:
Terms of use
- Copyright holder:
- Adam Paxton.
- Copyright date:
- 2020
- Rights statement:
- ©2020 The Author(s).
- 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/.
- Licence:
- CC Attribution (CC BY)
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