Some aspect of analysis on Riemannian manifolds

Abstract:

Singular integral operators are involved in the formulation and the solution of several problems in analysis. The classical theory of singular integrals was developed in the euclidean context. More recently, people have began to study singular integral on Riemannian manifolds. Here new interesting phenomena occur due to the interplay between analytic and geometric properties of the manifold. In this talk I shall present some recent results that illustrate this fact, concentrating in particular on Riesz transforms, a class of singular integrals that arises in the study of the regularity of solutions of elliptic equations.