2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55553A 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.31 pages, plain Tex. Paper prepared for the Fourth Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, September 1998High Energy Physics - Theorytext