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Harmonic maps into
Euclidean buildings and non-Archimedean superrigidity
Christine Breiner, Ben K Dees and Chikako Mese |
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Geometry & Topology 30 (2026) 2251–2296
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Abstract |
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We prove that harmonic maps into Euclidean buildings, which include -buildings, have singular sets of Hausdorff codimension 2, extending the locally finite regularity result of Gromov and Schoen. As an application, we prove superrigidity for algebraic groups over fields with non-Archimedean valuation, thereby generalizing the rank- -adic superrigidity results of Gromov and Schoen and casting the Bader–Furman generalization of Margulis’ higher-rank superrigidity result in a geometric setting. We also prove an existence theorem for a pluriharmonic map from a Kähler manifold to a Euclidean building. |
Keywords
harmonic maps, superrigidity, Euclidean buildings
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Mathematical Subject Classification
Primary: 53C43, 58E20
Secondary: 22E40, 22E50
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References |
Publication
Received: 30 August 2024
Revised: 2 February 2026
Accepted: 11 March 2026
Published: 31 July 2026
Proposed: Tobias H Colding
Seconded: David Fisher, Bruce Kleiner
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Authors |
| Christine Breiner | |
| Department of Mathematics Brown University Providence, RI United States |
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| Ben K Dees | |
| Department of Mathematics Brown University Providence, RI United States |
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| Chikako Mese | |
| Department of Mathematics Johns Hopkins University Baltimore, MD United States |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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