English

Compactness Theorems and Degree Theory for MOTS

Differential Geometry 2011-08-30 v3

Abstract

We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for MOTS. Moreover, the Compactness Theorem will allow us to adapt the recent Degree Theory of H. Rosenberg and G. Smith for proving existence results for embedded MOTS in suitable compact initial data sets

Keywords

Cite

@article{arxiv.1105.5805,
  title  = {Compactness Theorems and Degree Theory for MOTS},
  author = {José M. Espinar},
  journal= {arXiv preprint arXiv:1105.5805},
  year   = {2011}
}

Comments

The paper have been withdrawn since the cornerstone area estimate (Theorem 2.1 Ho, Pak Tung, "A first eigenvalue estimate for embedded hypersurfaces". Differential Geom. Appl. 26 (2008), no. 3, 273-276.) does not look right. Therefore, the author has decided to withdraw the paper

R2 v1 2026-06-21T18:14:13.825Z