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Elliptic PDEs on Compact Ricci Limit Spaces and Applications

Shouhei Honda Kyushu University, Fukuoka, Japan and Tohoku University, Sendai, Japan
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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 Electronic 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
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List Price: $117.00 MAA Member Price:$105.30
AMS Member Price: $70.20 Click above image for expanded view Elliptic PDEs on Compact Ricci Limit Spaces and Applications Shouhei Honda Kyushu University, Fukuoka, Japan and Tohoku University, Sendai, Japan Available Formats:  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
 Electronic 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 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$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.

• 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

• Requests

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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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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