Martedì 16 aprile alle 14:30 in aula Dottorato

 

presso il Dipartimento di Matematica

 

il Dott. Giona Veronelli
Università di Milano-Bicocca

 

terrà il seguente seminario:

“Distance-like functions and Sobolev spaces on manifolds”

Abstract: Let (M,g) be a complete non-compact Riemannian manifold. The distance function r(x) from a fixed reference point in general fails to be everywhere differentiable. We seek for geometric assumptions which garantee the existence of a function H on M which is smooth, distance-like (i.e. r(x)/C < H(x) < Cr(x) outside a compact set) and whose derivatives are bounded up to a certain order. We will present classical results and some more recent answers to this problem. As we will see distance-like functions permit to prove the density of smooth compactly supported functions in Sobolev spaces on manifolds, and to generalize to M other analytical tools and properties which are well known in the Euclidean space.