Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Xiong, Yuanpu"'
Autor:
Xiong, Yuanpu
Let $\Omega$ be a convex domain in $\mathbb{C}^n$ and $\varphi$ a convex function on $\Omega$. We prove that $\log{K_{\Omega,\varphi}(z)}$ is a convex function (might be identically $-\infty$) on $\Omega$, where $K_{\Omega,\varphi}$ is the weighted B
Externí odkaz:
http://arxiv.org/abs/2407.19254
In this paper, we study the relationship between the type problem and the asymptotic behaviour of the first (Dirichlet) eigenvalues $\lambda_1(B_r)$ of ``balls'' $B_r:=\{\rho
Externí odkaz:
http://arxiv.org/abs/2403.19086
Autor:
Chen, Bo-Yong, Xiong, Yuanpu
In this paper, we study the relationship between the type problem and the asymptotic behavior of the first eigenvalues $\lambda_1(B_r)$ of ``balls'' $B_r:=\{\rho
Externí odkaz:
http://arxiv.org/abs/2401.11803
Autor:
Xiong, Yuanpu
We find a precise relationship between the minimal extensions in $L^2$ and $L^p$ Ohsawa-Takegoshi extension theorems. This relationship also gives another proof to the $L^p$ version of the Ohsawa-Takegoshi extension theorem, which is different from t
Externí odkaz:
http://arxiv.org/abs/2308.08212
We present an equality between the Bergman metric and Carath\'{e}odry metric.
Externí odkaz:
http://arxiv.org/abs/2308.02359
Autor:
Xiong, Yuanpu, Zheng, Zhiyuan
We contruct two classes of Zalcman-type domains, on which the Bergman distance functions have certain pre-described boundary behaviors. Such examples also lead to generalizations of uniformly perfectness in the sense of Pommerenke. These weakly unifo
Externí odkaz:
http://arxiv.org/abs/2303.03241
Autor:
Chen, Bo-Yong, Xiong, Yuanpu
We show that the $p-$Bergman kernel $K_p(z)$ on a bounded domain $\Omega$ is of locally $C^{1,1}$ for $p\geq1$.The proof is based on the locally Lipschitz continuity of the off-diagonal $p-$Bergman kernel $K_p(\zeta,z)$ for fixed $\zeta\in \Omega$. G
Externí odkaz:
http://arxiv.org/abs/2302.06877
Autor:
Chen, Bo-Yong, Xiong, Yuanpu
The $p-$Bergman kernel $K_p(\cdot)$ is shown to be of $C^{1,1/2}$ for $1
Externí odkaz:
http://arxiv.org/abs/2208.01915
Autor:
Chen, Bo-Yong, Xiong, Yuanpu
We obtain a psh Hopf lemma for domains satisfying certain cusp conditions by using a sharp estimate for the Green function of a planar cusp along the axis. As an application, we obtain a negative psh exhaustion function with certain global growth est
Externí odkaz:
http://arxiv.org/abs/2112.09480
Autor:
Chen, Bo-Yong, Xiong, Yuanpu
Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle $L$ over $M$
Externí odkaz:
http://arxiv.org/abs/1907.11873