Min-max for phase transitions and the existence of embedded minimal hypersurfaces
Differential Geometry
2015-05-29 v2 Analysis of PDEs
Abstract
Strong parallels can be drawn between the theory of minimal hypersurfaces and the theory of phase transitions. Borrowing ideas from the former we extend recent results on the regularity of stable phase transition interfaces to the finite Morse index case. As an application we present a PDE-based proof of the celebrated theorem of Almgren-Pitts, on the existence of embedded minimal hypersurfaces in compact manifolds. We compare our results with other min-max theories.
Keywords
Cite
@article{arxiv.1505.06698,
title = {Min-max for phase transitions and the existence of embedded minimal hypersurfaces},
author = {Marco A. M. Guaraco},
journal= {arXiv preprint arXiv:1505.06698},
year = {2015}
}
Comments
41 pages, 4 figures