Elliptic PDEs on compact Ricci limit spaces and applications / Shouhei Honda.

Format:

Book

Author/Creator:

Honda, Shouhei, author.

Series:

Memoirs of the American Mathematical Society ; Number 1211.

Memoirs of the American Mathematical Society, 1947-6221 ; Number 1211

Language:

English

Subjects (All):

Geometry, Differential.

Physical Description:

1 online resource (104 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

"In this paper we study elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular we establish 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. We apply these to the study of second-order differential calculus on such limit spaces"-- Provided by publisher.

Contents:

Preliminaries

Lp-convergence revisited

Poisson's equations

Rellich type compactness for tensor fields

Differential forms.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4417-8