| 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 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 253; 2018; 92 ppMSC: 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
-
RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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
