Green functions for the Dirac operator under local boundary conditions and applications

Details Green functions for the Dirac operator under local boundary conditions and applications Green functions for the Dirac operator under local boundary conditions and applications

2007-03-07

arxiv.org/abs/math/0703197v1

Mathematics

Differential Geometry

23 pages

Scientific paper

In this paper, 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 particular, solve the Yamabe problem on manifolds with boundary in some cases. Finally, using the $\MIT$ Green function, we give a simple proof of a positive mass theorem previously proved by Escobar.

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