A Sobolev-like inequality for the Dirac operator
arXiv:0804.1024 · doi:10.1016/j.jfa.2008.11.007
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.
some typos corrected, the introduction has been rewritten and several references has been added, to appear in Journal of Functional Analysis