Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.19254 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912879770337280 |
|---|---|
| author | Xiong, Yuanpu |
| author_facet | Xiong, Yuanpu |
| contents | Let $Ω$ be a convex domain in $\mathbb{C}^n$ and $φ$ a convex function on $Ω$. We prove that $\log{K_{Ω,φ}(z)}$ is a convex function (might be identically $-\infty$) on $Ω$, where $K_{Ω,φ}$ is the weighted Bergman kernel. When $φ\equiv0$, we prove a Brunn-Minkowski type inequality, which further implies that $K_Ω(z)^{-\frac{1}{2n}}$ is a convex function if $Ω$ is convex. Some necessary and sufficient conditions for strictly convexity are also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19254 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convexity of the Bergman Kernels on Convex Domains Xiong, Yuanpu Complex Variables Let $Ω$ be a convex domain in $\mathbb{C}^n$ and $φ$ a convex function on $Ω$. We prove that $\log{K_{Ω,φ}(z)}$ is a convex function (might be identically $-\infty$) on $Ω$, where $K_{Ω,φ}$ is the weighted Bergman kernel. When $φ\equiv0$, we prove a Brunn-Minkowski type inequality, which further implies that $K_Ω(z)^{-\frac{1}{2n}}$ is a convex function if $Ω$ is convex. Some necessary and sufficient conditions for strictly convexity are also obtained. |
| title | Convexity of the Bergman Kernels on Convex Domains |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2407.19254 |