Green functions for the Dirac operator under local boundary conditions and applications |
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Authors: | Simon Raulot |
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Institution: | 1.Laboratoire de Mathématiques Rapha?l Salem, UMR 6085 CNRS,Université de Rouen,Saint Etienne du Rouvray,France |
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Abstract: | In this article, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated
with a chirality operator (also called the chiral bag boundary condition) and the MIT bag boundary condition. Then we give
some applications of these constructions for each Green function. From the existence of the chiral Green function, we derive
an inequality on a spin conformal invariant which, in some cases, solves the Yamabe problem on manifolds with boundary. Finally,
using the MIT Green function, we give a simple proof of a positive mass theorem previously proved by Escobar. |
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