Calculus of Variations and Geometric Measure Theory

A Feynman-Kac formula on manifolds with boundary and geometric applications

Levi Lopes de Lima

created by malchiodi on 06 Feb 2018
modified on 08 Feb 2018

8 feb 2018 -- 16:30   [open in google calendar]

Scuola Normale Superiore, Aula Capitini



We present a Feynman-Kac-type formula for the heat semigroup associated to a generalized Laplacian operator acting on sections of a vector bundle over a noncompact manifold with a (possibly noncompact) boundary under mixed boundary conditions. We discuss geometric applications of the formula including: i) a new obstruction to the existence of metrics with positive isotropic curvature and 2-convex boundary on compact manifolds; ii) a conservation property for the heat semigroup associated to a class of generalized Dirac Laplacians which extends previous results by Vesentini and Masamune in the setting of differential forms.