Harmonic maps and framed $\mathrm{PSL}_2(\mathbb{C})$-representations
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913991083687936 |
|---|---|
| author | Gupta, Subhojoy Sau, Gobinda |
| author_facet | Gupta, Subhojoy Sau, Gobinda |
| contents | We show that given an element $X$ of the enhanced Teichmüller space $\mathcal{T}^\pm(\mathbb{S}, \mathbb{M})$ and a type-preserving framed $\mathrm{PSL}_2(\mathbb{C})$-representation $\hatρ = (ρ,β)$, there is a $ρ$-equivariant harmonic map $f:\mathbb{H}^2 \to \mathbb{H}^3$ that is asymptotic to the framing $β$. Here, the domain is the universal cover of the punctured Riemann surface obtained from a conformal completion of $X$. Moreover, such a harmonic map is unique if one prescribes, in addition, the principal part of the Hopf differential at each puncture. The proof uses the harmonic map heat flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic maps and framed $\mathrm{PSL}_2(\mathbb{C})$-representations Gupta, Subhojoy Sau, Gobinda Differential Geometry Geometric Topology We show that given an element $X$ of the enhanced Teichmüller space $\mathcal{T}^\pm(\mathbb{S}, \mathbb{M})$ and a type-preserving framed $\mathrm{PSL}_2(\mathbb{C})$-representation $\hatρ = (ρ,β)$, there is a $ρ$-equivariant harmonic map $f:\mathbb{H}^2 \to \mathbb{H}^3$ that is asymptotic to the framing $β$. Here, the domain is the universal cover of the punctured Riemann surface obtained from a conformal completion of $X$. Moreover, such a harmonic map is unique if one prescribes, in addition, the principal part of the Hopf differential at each puncture. The proof uses the harmonic map heat flow. |
| title | Harmonic maps and framed $\mathrm{PSL}_2(\mathbb{C})$-representations |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2508.10335 |