Potential Theory on Gromov Hyperbolic Spaces-Reference-Cited by-同舟云学术

Potential Theory on Gromov Hyperbolic Spaces

Published:2022-01-01 Issue:1 Volume:10 Page:394-431
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:en
Short-container-title:

Author:

Kemper Matthias¹,Lohkamp Joachim¹

Affiliation:

1. Mathematisches Institut , Universität Münster , Münster , Germany

Abstract

Abstract Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov hyperbolic metric measure spaces, unifying these settings in a common framework ready for applications to singular spaces such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack inequalities and a complete classification of positive harmonic functions in terms of the Martin boundary which is identified with the geometric Gromov boundary.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2022-0147/pdf

Reference53 articles.

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