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Contraction property on complex hyperbolic ball

Autor: Li, Xiaoshan, Su, Guicong

We prove two isoperimetric inequalities on complex hyperbolic ball. As an application, we prove a contraction property for the holomorphic functions in Hardy and weighted Bergman spaces on the unit ball, thus extending the results of Kulikov (GAFA(20

Externí odkaz: http://arxiv.org/abs/2411.01911

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VCEMO: Multi-Modal Emotion Recognition for Chinese Voiceprints

Autor: Tang, Jinghua, Zhang, Liyun, Lu, Yu, Ding, Dian, Yang, Lanqing, Chen, YiChao, Bian, Minjie, Li, Xiaoshan, Xue, Guangtao

Emotion recognition can enhance humanized machine responses to user commands, while voiceprint-based perception systems can be easily integrated into commonly used devices like smartphones and stereos. Despite having the largest number of speakers, t

Externí odkaz: http://arxiv.org/abs/2408.13019

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$G$-invariant Bergman kernel and geometric quantization on complex manifolds with boundary

Autor: Hsiao, Chin-Yu, Huang, Rung-Tzung, Li, Xiaoshan, Shao, Guokuan

Publikováno v: Math. Ann. 2024

Let $M$ be a complex manifold with boundary $X$, which admits a holomorphic Lie group $G$-action preserving $X$. We establish a full asymptotic expansion for the $G$-invariant Bergman kernel under certain assumptions. As an application, we get $G$-in

Externí odkaz: http://arxiv.org/abs/2305.00601

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Semi-classical asymptotics of partial Bergman kernels on $\mathbb{R}$-symmetric complex manifolds with boundary

Autor: Hsiao, Chin-Yu, Li, Xiaoshan, Marinescu, George

Let $M$ be a relatively compact connected open subset with smooth connected boundary of a complex manifold $M'$. Let $(L,h^L)\rightarrow M'$ be a positive line bundle over $M'$. Suppose that $M'$ admits a holomorphic $\mathbb{R}$-action which preserv

Externí odkaz: http://arxiv.org/abs/2208.12412

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On Bergman kernel functions and weak Morse inequalities

Autor: Li, Xiaoshan, Shao, Guokuan, Wang, Huan

Publikováno v: Anal.Math.Phys. 13, 68 (2023)

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the asymptotic Bergma

Externí odkaz: http://arxiv.org/abs/2208.01994

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