Energy of harmonic functions and Gromov's proof of Stallings' theorem
Michael Kapovich
TL;DR
This paper details Gromov's proof of Stallings' theorem on groups with infinitely many ends, focusing on harmonic functions and a key compactness theorem for their family.
Contribution
It provides a detailed exposition of Gromov's approach, including a new compactness theorem for harmonic functions related to group ends.
Findings
Establishment of a compactness theorem for harmonic functions
Clarification of Gromov's proof of Stallings' theorem
Enhanced understanding of harmonic functions in group theory
Abstract
We provide the details for Gromov's proof of Stallings' theorem on groups with infinitely many ends using harmonic functions. The main technical result of the paper is a compactness theorem for a certain family of harmonic functions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Advanced Operator Algebra Research