Maximum Principles and Geometric Applications (Springer Monographs in Mathematics) - Softcover

Buch 139 von 187: Springer Monographs in Mathematics

Alías, Luis J.; Mastrolia, Paolo; Rigoli, Marco

 
9783319796055: Maximum Principles and Geometric Applications (Springer Monographs in Mathematics)
Softcover
ISBN 10: 3319796054 ISBN 13: 9783319796055
Verlag: Springer, 2019

Inhaltsangabe

This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. 

In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on.

Maximum Principles and GeometricApplications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter.

In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on.

Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
3319796054
ISBN 13 
9783319796055
Einband
Taschenbuch
Anzahl der Seiten
600
Kontakt zum Hersteller
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Darmstadt
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Deutschland

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Vorgestellte Ausgabe

ISBN 10:  3319243357 ISBN 13:  9783319243351
Verlag: Springer, 2016
Hardcover