On the Possible Orders of Harmonic Maps into Euclidean Buildings

Christine Breiner; Ben K. Dees

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arXiv · 2604.16608

On the Possible Orders of Harmonic Maps into Euclidean Buildings

Christine Breiner·Ben K. Dees

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Abstract

We prove a discreteness result for the possible orders of harmonic maps from surfaces to Euclidean buildings; in particular for a building of type $W$ the order is of the form $\frac mk$ where $k$ divides $|W|$. This generalizes, in the case where the domain has dimension $2$, the "order gap" of Gromov and Schoen. This result follows by directly analyzing the behavior of homogeneous maps into Euclidean buildings, and then studying a related spherical billiards problem.

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BibTeX RIS

Christine Breiner, Ben K. Dees. 2026-04-17. On the Possible Orders of Harmonic Maps into Euclidean Buildings. https://arxiv.org/abs/2604.16608

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