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Maximum principles and geometric applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Maximum principles and geometric applications/ by Luis J. Alias, Paolo Mastrolia, Marco Rigoli.
作者:	Alias, Luis J.
其他作者:	Mastrolia, Paolo.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xxvii, 570 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Maximum principles (Mathematics) -
電子資源:	http://dx.doi.org/10.1007/978-3-319-24337-5
ISBN:	9783319243375

Maximum principles and geometric applications
Alias, Luis J.

Maximum principles and geometric applications[electronic resource] /by Luis J. Alias, Paolo Mastrolia, Marco Rigoli. - Cham :Springer International Publishing :2016. - xxvii, 570 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

A crash course in Riemannian geometry -- The Omori-Yau maximum principle -- New forms of the maximum principle -- Sufficient conditions for the validity of the weak maximum principle -- Miscellany results for submanifolds -- Applications to hypersurfaces -- Hypersurfaces in warped products -- Applications to Ricci Solitons -- Spacelike hypersurfaces in Lorentzian spacetimes.

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.

ISBN: 9783319243375

Standard No.: 10.1007/978-3-319-24337-5doiSubjects--Topical Terms:

700590
Maximum principles (Mathematics)

LC Class. No.: QA377

Dewey Class. No.: 515.353

Maximum principles and geometric applications
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505 0 $a A crash course in Riemannian geometry -- The Omori-Yau maximum principle -- New forms of the maximum principle -- Sufficient conditions for the validity of the weak maximum principle -- Miscellany results for submanifolds -- Applications to hypersurfaces -- Hypersurfaces in warped products -- Applications to Ricci Solitons -- Spacelike hypersurfaces in Lorentzian spacetimes.
520 $a 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.
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