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
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The paper have been withdrawn since the cornerstone area estimate (Theorem 2.1 Ho, Pak Tung, "A first eigenvalue estimate for embedded hypersurfaces".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