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Affine Bernstein Problems And Monge-ampère Equations

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Title: Affine Bernstein Problems And Monge-ampère Equations
Description: In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Ampère equations.From the methodical point of view, it introduces the solution of certain Monge-Ampère equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.
Authors: An-min Li, Fang Jia, Udo Simon, Ruiwei Xu
Resource Type: eBook.
Subjects: Monge-Ampe`re equations, Affine differential geometry
Categories: MATHEMATICS / Geometry / Analytic, MATHEMATICS / Differential Equations / General
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 340794
RelevancyScore: 1031
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1031.17456054688
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  Data: Affine Bernstein Problems And Monge-ampère Equations
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  Label: Description
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  Data: In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Ampère equations.From the methodical point of view, it introduces the solution of certain Monge-Ampère equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.
– Name: Author
  Label: Authors
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  Data: <searchLink fieldCode="AR" term="%22An-min+Li%22">An-min Li</searchLink><br /><searchLink fieldCode="AR" term="%22Fang+Jia%22">Fang Jia</searchLink><br /><searchLink fieldCode="AR" term="%22Udo+Simon%22">Udo Simon</searchLink><br /><searchLink fieldCode="AR" term="%22Ruiwei+Xu%22">Ruiwei Xu</searchLink>
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  Data: eBook.
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  Data: <searchLink fieldCode="DE" term="%22Monge-Ampe%27re+equations%22">Monge-Ampe`re equations</searchLink><br /><searchLink fieldCode="DE" term="%22Affine+differential+geometry%22">Affine differential geometry</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 516.36
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Monge-Ampe`re equations
        Type: general
      – SubjectFull: Affine differential geometry
        Type: general
    Titles:
      – TitleFull: Affine Bernstein Problems And Monge-ampère Equations
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: An-min Li
      – PersonEntity:
          Name:
            NameFull: Fang Jia
      – PersonEntity:
          Name:
            NameFull: Udo Simon
      – PersonEntity:
          Name:
            NameFull: Ruiwei Xu
      – PersonEntity:
          Name:
            NameFull: An-min Li
      – PersonEntity:
          Name:
            NameFull: Fang Jia
      – PersonEntity:
          Name:
            NameFull: Udo Simon
      – PersonEntity:
          Name:
            NameFull: Ruiwei Xu
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2010
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9789812814166
            – Type: isbn-electronic
              Value: 9789812814173
          Titles:
            – TitleFull: Affine Bernstein Problems And Monge-ampère Equations
              Type: main
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