A new notion of subharmonicity on locally smoothing spaces, and a conjecture by Braverman, Milatovic, Shubin
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910399945768960 |
|---|---|
| author | Güneysu, Batu Pigola, Stefano Stollmann, Peter Veronelli, Giona |
| author_facet | Güneysu, Batu Pigola, Stefano Stollmann, Peter Veronelli, Giona |
| contents | Given a strongly local Dirichlet space and $λ\geq 0$, we introduce a new notion of $λ$--subharmonicity for $L^1_\loc$--functions, which we call \emph{local $λ$--shift defectivity}, and which turns out to be equivalent to distributional $λ$--subharmonicity in the Riemannian case. We study the regularity of these functions on a new class of strongly local Dirichlet, so called locally smoothing spaces, which includes Riemannian manifolds (without any curvature assumptions), finite dimensional RCD spaces, Carnot groups, and Sierpinski gaskets. As a byproduct of this regularity theory, we obtain in this general framework a proof of a conjecture by Braverman, Milatovic, Shubin on the positivity of distributional $L^q$-solutions of $Δf\leq f$ for complete Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09423 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new notion of subharmonicity on locally smoothing spaces, and a conjecture by Braverman, Milatovic, Shubin Güneysu, Batu Pigola, Stefano Stollmann, Peter Veronelli, Giona Analysis of PDEs Differential Geometry Metric Geometry Probability Given a strongly local Dirichlet space and $λ\geq 0$, we introduce a new notion of $λ$--subharmonicity for $L^1_\loc$--functions, which we call \emph{local $λ$--shift defectivity}, and which turns out to be equivalent to distributional $λ$--subharmonicity in the Riemannian case. We study the regularity of these functions on a new class of strongly local Dirichlet, so called locally smoothing spaces, which includes Riemannian manifolds (without any curvature assumptions), finite dimensional RCD spaces, Carnot groups, and Sierpinski gaskets. As a byproduct of this regularity theory, we obtain in this general framework a proof of a conjecture by Braverman, Milatovic, Shubin on the positivity of distributional $L^q$-solutions of $Δf\leq f$ for complete Riemannian manifolds. |
| title | A new notion of subharmonicity on locally smoothing spaces, and a conjecture by Braverman, Milatovic, Shubin |
| topic | Analysis of PDEs Differential Geometry Metric Geometry Probability |
| url | https://arxiv.org/abs/2302.09423 |