Prescribing Scalar Curvature in Conformal Geometry.

Format:

Book

Author/Creator:

Malchiodi, Author.

Series:

Zurich lectures in advanced mathematics.

Zurich Lectures in Advanced Mathematics (zlam) 31 2943-4971

Language:

English

Subjects (All):

Conformal geometry.

Physical Description:

1 online resource (161 pages)

Edition:

Second edition.

Place of Publication:

EMS Press 2023

Berlin : European Mathematical Society, [2023]

System Details:

text file PDF

Summary:

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.

ISBN:

9783985475520