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New Results in Heat-Kernel Asymptotics on Manifolds with Boundary

Giampiero V. M. Esposito

Abstract

A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and other functorial methods to the evaluation of heat-kernel coefficients; conditions for strong ellipticity of the boundary-value problem; fourth-order operators on manifolds with boundary; non-local boundary conditions in Euclidean quantum gravity. Many deep developments in physics and mathematics are therefore in sight.

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Key concepts: Heat kernel, Boundary value problem, Boundary (topology), Mathematics, Conformal map, Mathematical analysis, Euclidean geometry, Boundary conformal field theory