Prescribing Scalar Curvature in Conformal Geometry

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 chal...

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Opis bibliograficzny
1. autor: Malchiodi, Andrea, 1972-
Format: Livre numérique
Język:Anglais
Wydane: Berlin : European Mathematical Society 2023.
Berlin :
Seria:Zurich Lectures in Advanced Mathematics
Dostęp online:Accès sur la plateforme EMS Press
Accès sur la plateforme ISTEX
Accès Université d'Orléans
Accès INSA CVL
Komentarz: European Mathematical Society (Licence nationale)
European Mathematical Society (Licence nationale)
Autres localisations: Voir dans le Sudoc
Edition sous un autre format:• Prescribing Scalar Curvature in Conformal Geometry, 978-3-98547-052-5
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520 |a 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. 
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