# 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 ...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Version of record, 1.1MB)
Publisher copy:
10.1007/s00023-020-00939-9

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Physics
Role:
Author
Publisher:
Springer Publisher's website
Journal:
Annales Henri Poincaré Journal website
Volume:
21
Issue:
9
Pages:
3035–3068
Publication date:
2020-07-24
Acceptance date:
2020-07-10
DOI:
EISSN:
1424-0661
ISSN:
1424-0637
Language:
English
Keywords:
Pubs id:
1126412
Local pid:
pubs:1126412
Deposit date:
2020-10-01