2007/03/07 by Simon Raulot, Raulot, Simon · 1 citation
Computer Science · Mathematics · #53A30 #53C27 (Primary) #58C40 (Secondary) #58J50 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.DG #msc:53A30 #msc:53C27 #msc:58C40 #msc:58J50
paper · pdf · doi:10.48550/arxiv.math/0703197
23 pages
arxiv created 2007/03/07 · openalex publication_date 2007/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.