On the Possible Orders of Harmonic Maps into Euclidean Buildings
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911603328286720 |
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| author | Breiner, Christine Dees, Ben K. |
| author_facet | Breiner, Christine Dees, Ben K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16608 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Possible Orders of Harmonic Maps into Euclidean Buildings Breiner, Christine Dees, Ben K. Differential Geometry 53C43, 58E20 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. |
| title | On the Possible Orders of Harmonic Maps into Euclidean Buildings |
| topic | Differential Geometry 53C43, 58E20 |
| url | https://arxiv.org/abs/2604.16608 |