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Energy of harmonic functions and Gromov's proof of Stallings' theorem
Veröffentlicht/Copyright:
26. Juli 2014
Abstract
We provide 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.
Keywords: Harmonic functions; ends of groups
Funding source: NSF
Award Identifier / Grant number: DMS-12-05312
This paper was motivated by numerous discussions with Mohan Ramachandran, to whom I am grateful for many valuable references and suggestions as well as the proof of Theorem 9.1. I am grateful to P. Li and W. Woess for useful remarks and references.
Received: 2014-6-21
Accepted: 2014-7-8
Published Online: 2014-7-26
Published in Print: 2014-9-1
© 2014 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- A class of differential equations of fractional order with multi-point boundary conditions
- Complex structures in algebra, topology and differential equations
- Normality and the differential polynomial of meromorphic functions
- Characterization of the Robin function by extremal problems
- Extension of the Schwarz Lemma to homeomorphisms with controlled p-module
- Energy of harmonic functions and Gromov's proof of Stallings' theorem
- A characterization of uncountable sets in terms of their self-mappings and large invariant subsets
- Positive solutions of periodic type boundary value problems for first order singular functional differential equations
- Milin's coefficients, complex geometry of Teichmüller spaces and variational calculus for univalent functions
- Potential flow and conformal distortion theory
- Variations on the theorems of F. and M. Riesz and of Hardy and Littlewood
- Information-preserving operators
- Boundedness of intrinsic square functions on generalized Morrey spaces
- Normal criteria of meromorphic functions and shared functions
Artikel in diesem Heft
- Frontmatter
- A class of differential equations of fractional order with multi-point boundary conditions
- Complex structures in algebra, topology and differential equations
- Normality and the differential polynomial of meromorphic functions
- Characterization of the Robin function by extremal problems
- Extension of the Schwarz Lemma to homeomorphisms with controlled p-module
- Energy of harmonic functions and Gromov's proof of Stallings' theorem
- A characterization of uncountable sets in terms of their self-mappings and large invariant subsets
- Positive solutions of periodic type boundary value problems for first order singular functional differential equations
- Milin's coefficients, complex geometry of Teichmüller spaces and variational calculus for univalent functions
- Potential flow and conformal distortion theory
- Variations on the theorems of F. and M. Riesz and of Hardy and Littlewood
- Information-preserving operators
- Boundedness of intrinsic square functions on generalized Morrey spaces
- Normal criteria of meromorphic functions and shared functions
