Elliptic PDEs on compact Ricci limit spaces and applications
著者
書誌事項
Elliptic PDEs on compact Ricci limit spaces and applications
（Memoirs of the American Mathematical Society, no. 1211）
American Mathematical Society, c2018
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注記
Includes bibliographical references
May 2018, volume 253, number 1211 (sixth of 7 numbers)
内容説明・目次
内容説明
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 Schrodinger 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.
目次
Introduction
Preliminaries
$L^p$-convergence revisited
Poisson's equations
Schrodinger operators and generalized Yamabe constants
Rellich type compactness for tensor fields
Differential forms
Bibliography.
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