Formula for the fundamental solution of the heat equation on the sphere

Abstract

This paper is devoted to the derivation of a simple asymptotic formula for the fundamental solution of the heat equation on the sphere. This formula is efficient for small values of the evolution parameter, and thus, complements the well-known formula for the fundamental solution in terms of Legendre polynomials that is efficient for relatively large values of the evolution parameter. The method relies on constructing a self-similar solution.