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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Maximum Principles and Geometric Applications (Hardcover, 1st ed. 2016)
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Maximum Principles and Geometric Applications (Hardcover, 1st ed. 2016)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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.
General
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