Prescribing Scalar Curvature In Conformal Geometry Andrea Malchiodi by Andrea Malchiodi 9783985475520, 9783985470525, 3985475520, 3985470529 instant download after payment.

This book treats the classical problem, posed by Kazdan and Warner, of prescribing a given function on a closed manifold as the scalar curvature of a metric within a conformal class. Since both critical equations and obstructions to the existence of solutions appear, the problem is particularly challenging.
Our focus is to present a general approach for understanding the matter, particularly the issue of loss of compactness. The task of establishing existence of solutions is attacked combining several tools: the variational structure of the problem, Liouville-type theorems, blow-up analysis, elliptic regularity theory, and topological arguments.
Treating different aspects of the subject and containing several references to up-to-date research directions and perspectives, the book will be useful to graduate students and researchers interested in geometric analysis and partial differential equations.