A Sobolev-like inequality for the Dirac operator |
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Authors: | Simon Raulot |
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Institution: | Université de Neuchâtel, Institut de Mathématiques, Rue Emile-Argand 11, 2007 Neuchâtel, Switzerland |
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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. |
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Keywords: | Dirac operator Sobolev inequality Conformal geometry Nonlinear elliptic equations |
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