Short-time asymptotics of the heat kernel of the Laplacian of a bounded domain with Robin boundary conditions

The basic problem in this paper is that of determining some geometrical properties of a general bounded domain in two or three dimensions with a smooth boundary where smooth functions are entering the boundary conditions which are not strictly positive, from complete knowledge of the eigenvalues for the negative Laplacian, using the asymptotic expansions of the trace of the heat kernel for short-time t. Further results are obtained.