A Sobolev-like inequality for the Dirac operator
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2008
- DOI:
- 10.48550/arXiv.0804.1024
- arXiv:
- arXiv:0804.1024
- Bibcode:
- 2008arXiv0804.1024R
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- some typos corrected, the introduction has been rewritten and several references has been added, to appear in Journal of Functional Analysis