Weil--Petersson homeomorphisms, minimal lagrangian diffeomorphisms, and maximal surfaces in anti-de Sitter space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914489461374976 |
|---|---|
| author | Diaf, Farid Moriani, Alex Smaï, Rym Smith, Graham Andrew Trebeschi, Enrico |
| author_facet | Diaf, Farid Moriani, Alex Smaï, Rym Smith, Graham Andrew Trebeschi, Enrico |
| contents | In this paper, we study the class of Weil--Petersson circle homeomorphisms from the point of view of three-dimensional anti-de Sitter space $\mathbf{AdS}^{2,1}$. We show that a homeomorphism $φ:\mathbf{RP}^1\to\mathbf{RP}^1$ is Weil--Petersson if and only if its graph, viewed as a curve in the boundary at infinity of $\mathbf{AdS}^{2,1}$, is the asymptotic boundary of a complete maximal spacelike surface in $\mathbf{AdS}^{2,1}$ with finite renormalized area. As an application, we obtain the following AdS-independent result in Teichmüller theory: a homeomorphism is Weil--Petersson if and only if its minimal lagrangian extension to $\mathbf{H}^2$ has square-integrable Beltrami differential. We also provide two further new technical characterizations, which we believe to be of independent interest, and which are essential for the proofs of our main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weil--Petersson homeomorphisms, minimal lagrangian diffeomorphisms, and maximal surfaces in anti-de Sitter space Diaf, Farid Moriani, Alex Smaï, Rym Smith, Graham Andrew Trebeschi, Enrico Differential Geometry 30C62, 30F60, 53A10, 53C50 In this paper, we study the class of Weil--Petersson circle homeomorphisms from the point of view of three-dimensional anti-de Sitter space $\mathbf{AdS}^{2,1}$. We show that a homeomorphism $φ:\mathbf{RP}^1\to\mathbf{RP}^1$ is Weil--Petersson if and only if its graph, viewed as a curve in the boundary at infinity of $\mathbf{AdS}^{2,1}$, is the asymptotic boundary of a complete maximal spacelike surface in $\mathbf{AdS}^{2,1}$ with finite renormalized area. As an application, we obtain the following AdS-independent result in Teichmüller theory: a homeomorphism is Weil--Petersson if and only if its minimal lagrangian extension to $\mathbf{H}^2$ has square-integrable Beltrami differential. We also provide two further new technical characterizations, which we believe to be of independent interest, and which are essential for the proofs of our main results. |
| title | Weil--Petersson homeomorphisms, minimal lagrangian diffeomorphisms, and maximal surfaces in anti-de Sitter space |
| topic | Differential Geometry 30C62, 30F60, 53A10, 53C50 |
| url | https://arxiv.org/abs/2604.17804 |