rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Maximum Principles and Geometric Applications
  name:
    name part: Alías, Luis J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Mastrolia, Paolo.
    role:
      role term: author.
  name:
    name part: Rigoli, Marco.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    edition: 1st ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVII, 570 p. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Luis J. Alías, Paolo Mastrolia, Marco Rigoli.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Partial differential equations
  subject:
    topic: Geometry
  subject:
    topic: Mathematics
  subject:
    topic: Global Analysis and Analysis on Manifolds
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Geometry
  classification: QA614-614.97
  classification: 514.74
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9783319243375
  identifier: http://dx.doi.org/10.1007/978-3-319-24337-5
  record info:
    record creation date: 160213
    record change date: 20160213075911.0
    record identifier: 978-3-319-24337-5