Prescribing Scalar Curvature in Conformal Geometry
Seiten
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.
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.
Scuola Normale Superiore di Pisa, Italy
| Erscheinungsdatum | 14.09.2023 |
|---|---|
| Reihe/Serie | Zurich Lectures in Advanced Mathematics ; 31 |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | blow-up analysis • elliptic equations of critical type • prescribed scalar curvature • topological methods |
| ISBN-10 | 3-98547-052-9 / 3985470529 |
| ISBN-13 | 978-3-98547-052-5 / 9783985470525 |
| Zustand | Neuware |
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