Mathematics
Stable surfaces and free boundary marginally outer trapped surfaces
Document Type
Article
Abstract
We explore various notions of stability for surfaces embedded and immersed in spacetimes and initial data sets. The interest in such surfaces lies in their potential to go beyond the variational techniques which often underlie the study of minimal and CMC surfaces. We prove two versions of Christodoulou–Yau estimate for H-stable surfaces, a Cohn-Vossen type inequality for non-compact stable marginally outer trapped surface (MOTS), and a global theorem on the topology of H-stable surfaces. Moreover, we give a definition of capillary stability for MOTS with boundary. This notion of stability leads to an area upper bound inequality and a local splitting theorem for free boundary stable MOTS. Finally, we establish an index estimate and a diameter estimate for free boundary MOTS. These are straightforward generalizations of Chen–Fraser–Pang and Carlotto–Franz results for free boundary minimal surfaces, respectively.
Publication Title
Calculus of Variations and Partial Differential Equations
Publication Date
10-2021
Volume
60
Issue
5
ISSN
0944-2669
DOI
10.1007/s00526-021-02063-w
Keywords
black holes, initial datum, manifold
Repository Citation
Alaee, Aghil; Lesourd, Martin; and Yau, Shing Tung, "Stable surfaces and free boundary marginally outer trapped surfaces" (2021). Mathematics. 45.
https://commons.clarku.edu/mathematics/45
