Surface to surface changes of variables and applications

Abstract

The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration process is affected by a surface to surface change of variables. We provide precise answers to these and other related issues, and discuss a number of applications, such as the invariance of Lebesgue and Sobolev spaces on surfaces..