Download this article
 Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
Other MSP Journals
Distances between fixed-point sets in metrically complete 2-dimensional Euclidean buildings are realised

Harris Leung, Jeroen Schillewaert and Anne Thomas

Vol. 20 (2023), No. 2-3, 341–351

We prove that if two finitely generated groups act by isometries on a metrically complete 2-dimensional Euclidean building, then the distance between their fixed-point sets is realised. Our proof uses the geometry of Euclidean buildings, which we view as CAT (0) spaces, and properties of ultrapowers of Euclidean buildings.

Euclidean buildings, fixed point sets, distance
Mathematical Subject Classification
Primary: 20E42
Received: 23 October 2022
Revised: 26 June 2023
Accepted: 17 July 2023
Published: 13 September 2023
Harris Leung
University of Auckland
New Zealand
Jeroen Schillewaert
University of Auckland
New Zealand
Anne Thomas
School of Mathematics and Statistics
University of Sydney