Min-max theory and minimal surfaces with prescribed genus
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909002149920768 |
|---|---|
| author | Chu, Adrian Chun-Pong Li, Yangyang Wang, Zhihan |
| author_facet | Chu, Adrian Chun-Pong Li, Yangyang Wang, Zhihan |
| contents | We establish a general min-max type theorem that produces minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature. An important intermediate step is to show that, in a generic metric with positive Ricci curvature, any family of smooth embedded surfaces, possibly with finitely many singularities, can be deformed into a certain topologically optimal family.
Results in this paper will be crucial to our program on the construction of multiple minimal surfaces with prescribed genus in 3-spheres via topological methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Min-max theory and minimal surfaces with prescribed genus Chu, Adrian Chun-Pong Li, Yangyang Wang, Zhihan Differential Geometry Analysis of PDEs Geometric Topology We establish a general min-max type theorem that produces minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature. An important intermediate step is to show that, in a generic metric with positive Ricci curvature, any family of smooth embedded surfaces, possibly with finitely many singularities, can be deformed into a certain topologically optimal family. Results in this paper will be crucial to our program on the construction of multiple minimal surfaces with prescribed genus in 3-spheres via topological methods. |
| title | Min-max theory and minimal surfaces with prescribed genus |
| topic | Differential Geometry Analysis of PDEs Geometric Topology |
| url | https://arxiv.org/abs/2507.23239 |