## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 171 - 188

### A fixed-point property of finitely generated groups and an energy of equivariant maps

#### Abstract

The purpose of this article is to present sufficient conditions for an isometric action of a finitely generated group to have a fixed point in terms of an energy of equivariant maps (Proposition 2.1 and Theorem 3.1), which turn out to be useful in proving that groups with fixed-point property form a large family in the set of finitely presented groups. Most of the results are included in [7] and [8].

#### Article information

**Source***Probabilistic Approach to Geometry*, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 171-188

**Dates**

Received: 24 January 2009

Revised: 4 March 2009

First available in Project Euclid:
24 November 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1543086318

**Digital Object Identifier**

doi:10.2969/aspm/05710171

**Mathematical Reviews number (MathSciNet)**

MR2648259

**Zentralblatt MATH identifier**

1201.58014

**Subjects**

Primary: 58E20: Harmonic maps [See also 53C43], etc. 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

**Keywords**

Fixed-point property finitely generated groups harmonic maps

#### Citation

Izeki, Hiroyasu. A fixed-point property of finitely generated groups and an energy of equivariant maps. Probabilistic Approach to Geometry, 171--188, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710171. https://projecteuclid.org/euclid.aspm/1543086318