A Sobolev-like inequality for the Dirac operator
Differential Geometry
2009-03-10 v2
Abstract
In this article, we prove a Sobolev-like inequality for the Dirac operator on closed compact Riemannian spin manifolds with a nearly optimal Sobolev constant. As an application, we give a criterion for the existence of solutions to a nonlinear equation with critical Sobolev exponent involving the Dirac operator. We finally specify a case where this equation can be solved.
Cite
@article{arxiv.0804.1024,
title = {A Sobolev-like inequality for the Dirac operator},
author = {Simon Raulot},
journal= {arXiv preprint arXiv:0804.1024},
year = {2009}
}
Comments
some typos corrected, the introduction has been rewritten and several references has been added, to appear in Journal of Functional Analysis