Synopses & Reviews
The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem, and to describe in a way accessible to non-specialists a range of methods and techniques that can be successfully applied to nonlinear differential equations in situations where the lack of compactness and of symmetry and homogeneity prevents the use of more standard tools typical of compact situations or of the Euclidean setting.
Synopsis
This monograph offers an introduction to some geometric and analytic aspects of the Yamabe problem, which is accessible to non-specialists in the field. It presents a number of new results and techniques as well as new proofs of known results.
Table of Contents
Introduction.- 1 Some Riemannian Geometry.- 2 Pointwise conformal metrics.- 3 General nonexistence results.- 4 A priori estimates.- 5 Uniqueness.- 6 Existence.- 7 Some special cases.- References.- Index.