Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914919623950336 |
|---|---|
| author | Pakzad, Mohammad Reza |
| author_facet | Pakzad, Mohammad Reza |
| contents | We prove that the image of an isometric embedding into ${\mathbb R}^3$ of a two dimensionnal complete Riemannian manifold $(Σ, g)$ without boundary is a convex surface provided both the embedding and the metric $g$ enjoy a $C^{1,α}$ regularity for some $α>2/3$ and the distributional Gaussian curvature of $g$ is nonnegative and nonzero. The analysis must pass through some key observations regarding solutions to the very weak Monge-Ampère equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_09224 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature Pakzad, Mohammad Reza Differential Geometry Analysis of PDEs Functional Analysis 53A05, 53C24 53C21, 35J96 We prove that the image of an isometric embedding into ${\mathbb R}^3$ of a two dimensionnal complete Riemannian manifold $(Σ, g)$ without boundary is a convex surface provided both the embedding and the metric $g$ enjoy a $C^{1,α}$ regularity for some $α>2/3$ and the distributional Gaussian curvature of $g$ is nonnegative and nonzero. The analysis must pass through some key observations regarding solutions to the very weak Monge-Ampère equation. |
| title | Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature |
| topic | Differential Geometry Analysis of PDEs Functional Analysis 53A05, 53C24 53C21, 35J96 |
| url | https://arxiv.org/abs/2206.09224 |