Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
High-energy harmonic maps and degeneration of minimal surfaces

Charles Ouyang

Geometry & Topology 27 (2023) 1691–1746
Abstract

Let S be a closed surface of genus g 2 and ρ a maximal PSL (2, ) × PSL (2, ) surface group representation. By a result of Schoen, there is a unique ρ–equivariant minimal surface Σ~ in 2 × 2. We study the induced metrics on these minimal surfaces and prove the limits are precisely mixed structures. We prove a similar result for maximal surfaces in AdS 3. In the second half of the paper, we provide a geometric interpretation: the minimal surfaces Σ~ degenerate to the core of a product of two –trees. As a consequence, we obtain a compactification of the space of maximal representations of π1(S) into PSL (2, ) × PSL (2, ).

Keywords
minimal lagrangian, harmonic maps, mixed structures, higher Teichmüller space
Mathematical Subject Classification 2010
Primary: 49Q05, 53C43
References
Publication
Received: 6 January 2020
Revised: 25 July 2021
Accepted: 22 December 2021
Published: 27 July 2023
Proposed: Anna Wienhard
Seconded: Tobias H Colding, Mladen Bestvina
Authors
Charles Ouyang
Department of Mathematics
Washington University
St Louis, MO
United States

Open Access made possible by participating institutions via Subscribe to Open.