A Sobolev-like inequality for the Dirac operator

Details A Sobolev-like inequality for the Dirac operator A Sobolev-like inequality for the Dirac operator

2008-04-07

arxiv.org/abs/0804.1024v2

Journal of Functional Analysis 256, 5 (2009) 1588-1617

Mathematics

Differential Geometry

some typos corrected, the introduction has been rewritten and several references has been added, to appear in Journal of Funct

Scientific paper

10.1016/j.jfa.2008.11.007

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.

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