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

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dc.creatorRaulot, Simon
dc.date2007-03-07
dc.date.accessioned2026-07-07T07:50:40Z
dc.date.available2026-07-07T07:50:40Z
dc.descriptionIn 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.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0703197
dc.identifierhttp://arxiv.org/abs/math/0703197
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125238
dc.subjectDifferential Geometry
dc.subject53A30, 53C27 (Primary), 58J50, 58C40 (Secondary)
dc.titleGreen functions for the Dirac operator under local boundary conditions and applications
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