Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909256146485248 |
|---|---|
| author | Kar, Debaprasanna |
| author_facet | Kar, Debaprasanna |
| contents | We establish geometric upper and lower estimates for the Carathéodory and Kobayashi-Eisenman volume elements on the class of non-degenerate convex domains, as well as on the more general class of non-degenerate $\mathbb{C}$-convex domains. As a consequence, we obtain explicit universal lower bounds for the quotient invariant both on non-degenerate convex and $\mathbb{C}$-convex domains. Here the bounds we derive, for the above mentioned classes in $\mathbb{C}^{n}$, only depend on the dimension $n$ for a fixed $n\geq 2$. Finally, it is shown that the Bergman kernel is comparable with these volume elements up to small/large constants depending only on $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains Kar, Debaprasanna Complex Variables 32F45, 32F32, 32A25 We establish geometric upper and lower estimates for the Carathéodory and Kobayashi-Eisenman volume elements on the class of non-degenerate convex domains, as well as on the more general class of non-degenerate $\mathbb{C}$-convex domains. As a consequence, we obtain explicit universal lower bounds for the quotient invariant both on non-degenerate convex and $\mathbb{C}$-convex domains. Here the bounds we derive, for the above mentioned classes in $\mathbb{C}^{n}$, only depend on the dimension $n$ for a fixed $n\geq 2$. Finally, it is shown that the Bergman kernel is comparable with these volume elements up to small/large constants depending only on $n$. |
| title | Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains |
| topic | Complex Variables 32F45, 32F32, 32A25 |
| url | https://arxiv.org/abs/2401.05096 |