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Prescribing Scalar Curvature in Conformal Geometry

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Title: Prescribing Scalar Curvature in Conformal Geometry
Description: This book treats the classical problem, posed by Kazdan and Warner, of prescribing a given function on a closed manifold as the scalar curvature of a metric within a conformal class. Since both critical equations and obstructions to the existence of solutions appear, the problem is particularly challenging. Our focus is to present a general approach for understanding the matter, particularly the issue of loss of compactness. The task of establishing existence of solutions is attacked combining several tools: the variational structure of the problem, Liouville-type theorems, blow-up analysis, elliptic regularity theory, and topological arguments. Treating different aspects of the subject and containing several references to up-to-date research directions and perspectives, the book will be useful to graduate students and researchers interested in geometric analysis and partial differential equations.
Authors: Andrea Malchiodi
Resource Type: eBook.
Subjects: Conformal geometry, Curvature
Categories: MATHEMATICS / Geometry / Analytic, MATHEMATICS / Differential Equations / Partial
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 3808246
RelevancyScore: 1116
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1116.28857421875
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  Label: Title
  Group: Ti
  Data: Prescribing Scalar Curvature in Conformal Geometry
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This book treats the classical problem, posed by Kazdan and Warner, of prescribing a given function on a closed manifold as the scalar curvature of a metric within a conformal class. Since both critical equations and obstructions to the existence of solutions appear, the problem is particularly challenging. Our focus is to present a general approach for understanding the matter, particularly the issue of loss of compactness. The task of establishing existence of solutions is attacked combining several tools: the variational structure of the problem, Liouville-type theorems, blow-up analysis, elliptic regularity theory, and topological arguments. Treating different aspects of the subject and containing several references to up-to-date research directions and perspectives, the book will be useful to graduate students and researchers interested in geometric analysis and partial differential equations.
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  Data: <searchLink fieldCode="AR" term="%22Andrea+Malchiodi%22">Andrea Malchiodi</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Conformal+geometry%22">Conformal geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Curvature%22">Curvature</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 516.36
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Conformal geometry
        Type: general
      – SubjectFull: Curvature
        Type: general
    Titles:
      – TitleFull: Prescribing Scalar Curvature in Conformal Geometry
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Andrea Malchiodi
      – PersonEntity:
          Name:
            NameFull: Andrea Malchiodi
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2023
            – D: 26
              M: 03
              Type: profile
              Y: 2024
          Identifiers:
            – Type: isbn-print
              Value: 9783985470525
            – Type: isbn-electronic
              Value: 9783985475520
          Titles:
            – TitleFull: Prescribing Scalar Curvature in Conformal Geometry
              Type: main
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