Monotone Quantities for $p$-Harmonic functions and the Sharp $p$-Penrose inequality
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913199883812864 |
|---|---|
| author | Mazurowski, Liam Yao, Xuan |
| author_facet | Mazurowski, Liam Yao, Xuan |
| contents | Consider a complete asymptotically flat 3-manifold $M$ with non-negative scalar curvature and non-empty minimal boundary $Σ$. Fix a number $1 < p < 3$. We derive monotone quantities for $p$-harmonic functions on $M$ which become constant on Schwarzschild. These monotonicity formulas imply a sharp mass-capacity estimate relating the ADM mass of $M$ with the $p$-capacity of $Σ$ in $M$, which was first proved by Xiao using weak inverse mean curvature flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19784 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Monotone Quantities for $p$-Harmonic functions and the Sharp $p$-Penrose inequality Mazurowski, Liam Yao, Xuan Differential Geometry Mathematical Physics Classical Analysis and ODEs Consider a complete asymptotically flat 3-manifold $M$ with non-negative scalar curvature and non-empty minimal boundary $Σ$. Fix a number $1 < p < 3$. We derive monotone quantities for $p$-harmonic functions on $M$ which become constant on Schwarzschild. These monotonicity formulas imply a sharp mass-capacity estimate relating the ADM mass of $M$ with the $p$-capacity of $Σ$ in $M$, which was first proved by Xiao using weak inverse mean curvature flow. |
| title | Monotone Quantities for $p$-Harmonic functions and the Sharp $p$-Penrose inequality |
| topic | Differential Geometry Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2305.19784 |