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Elliptic PDEs on Compact Ricci Limit Spaces and Applications
 
Shouhei Honda Kyushu University, Fukuoka, Japan and Tohoku University, Sendai, Japan
Elliptic PDEs on Compact Ricci Limit Spaces and Applications
Softcover ISBN:  978-1-4704-2854-9
Product Code:  MEMO/253/1211
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4417-4
Product Code:  MEMO/253/1211.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2854-9
eBook: ISBN:  978-1-4704-4417-4
Product Code:  MEMO/253/1211.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
Elliptic PDEs on Compact Ricci Limit Spaces and Applications
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Elliptic PDEs on Compact Ricci Limit Spaces and Applications
Shouhei Honda Kyushu University, Fukuoka, Japan and Tohoku University, Sendai, Japan
Softcover ISBN:  978-1-4704-2854-9
Product Code:  MEMO/253/1211
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4417-4
Product Code:  MEMO/253/1211.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2854-9
eBook ISBN:  978-1-4704-4417-4
Product Code:  MEMO/253/1211.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2532018; 92 pp
    MSC: Primary 53

    In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. $L^p$-convergence revisited
    • 4. Poisson’s equations
    • 5. Schrödinger operators and generalized Yamabe constants
    • 6. Rellich type compactness for tensor fields
    • 7. Differential forms
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2532018; 92 pp
MSC: Primary 53

In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. $L^p$-convergence revisited
  • 4. Poisson’s equations
  • 5. Schrödinger operators and generalized Yamabe constants
  • 6. Rellich type compactness for tensor fields
  • 7. Differential forms
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.