Minimal Surface Entropy and Average Area Ratio
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913901724041216 |
|---|---|
| author | Lowe, Ben Neves, Andre |
| author_facet | Lowe, Ben Neves, Andre |
| contents | On any closed hyperbolizable 3-manifold, we find a sharp relation between the minimal surface entropy (introduced by Calegari-Marques-Neves) and the average area ratio (introduced by Gromov), and we show that, among metrics g with scalar curvature greater than or equal to -6, the former is maximized by the hyperbolic metric. One corollary is to solve a conjecture of Gromov regarding the average area ratio. Our proofs use Ricci flow with surgery and laminar measures invariant under a PSL(2,R)-action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_09451 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Minimal Surface Entropy and Average Area Ratio Lowe, Ben Neves, Andre Differential Geometry Dynamical Systems Geometric Topology 53A10, 57M50 On any closed hyperbolizable 3-manifold, we find a sharp relation between the minimal surface entropy (introduced by Calegari-Marques-Neves) and the average area ratio (introduced by Gromov), and we show that, among metrics g with scalar curvature greater than or equal to -6, the former is maximized by the hyperbolic metric. One corollary is to solve a conjecture of Gromov regarding the average area ratio. Our proofs use Ricci flow with surgery and laminar measures invariant under a PSL(2,R)-action. |
| title | Minimal Surface Entropy and Average Area Ratio |
| topic | Differential Geometry Dynamical Systems Geometric Topology 53A10, 57M50 |
| url | https://arxiv.org/abs/2110.09451 |