Prescribing Scalar Curvature in Conformal Geometry
Saved in:
| Title: | Prescribing Scalar Curvature in Conformal Geometry |
|---|---|
| Description: | 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. |
| Authors: | Andrea Malchiodi |
| Resource Type: | eBook. |
| Subjects: | Conformal geometry, Curvature |
| Categories: | MATHEMATICS / Geometry / Analytic, MATHEMATICS / Differential Equations / Partial |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | 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: | 9783985470525 9783985475520 |
