中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
多复变与复几何研讨班SCV&CG Seminar
Speaker: 李小山 副教授 (武汉大学)
Inviter: 周向宇
Language: Chinese
Title: Localization of Bergman Kernels and the Cheng-Yau Conjecture on Real Analytic Pseudoconvex Domains (I)
Time & Venue: 2026年5月26日（星期二） 10:00 - 11:30 & 南楼N913
Abstract:
This talk consists of two parts.
In the first part, we present our recent progress on the Cheng–Yau conjecture. The conjecture states that a smooth bounded pseudoconvex domain whose Bergman metric is Einstein must be biholomorphic to the unit ball. By employing a new localization theorem for the Bergman kernel on unbounded pseudoconvex domains, together with a recent result of Mir and Zaitsev, we prove this conjecture for domains with real-analytic boundary. In the smooth case, we prove the conjecture under the additional assumption that the domain is h-extendible.
In the second part, we discuss the two core tools used in the proof: the localization of the Bergman kernel for unbounded pseudoconvex domains near a D'Angelo finite type boundary point, and the existence of a weakly pseudoconvex h-extendible boundary point on a bounded real-analytic pseudoconvex domain whose Bergman metric is Kähler–Einstein. These results allow us to reduce the study to the h-extendible case.
The talk is based on joint work with Chin-Yu Hsiao and Xiaojun Huang.
Speaker: 李小山 副教授 (武汉大学)
Inviter: 周向宇
Language: Chinese
Title: Localization of Bergman Kernels and the Cheng-Yau Conjecture on Real Analytic Pseudoconvex Domains (II)
Time & Venue: 2026年5月27日（星期三） 19:00 - 20:30 & 南楼N913
Abstract:
This talk consists of two parts.
In the first part, we present our recent progress on the Cheng–Yau conjecture. The conjecture states that a smooth bounded pseudoconvex domain whose Bergman metric is Einstein must be biholomorphic to the unit ball. By employing a new localization theorem for the Bergman kernel on unbounded pseudoconvex domains, together with a recent result of Mir and Zaitsev, we prove this conjecture for domains with real-analytic boundary. In the smooth case, we prove the conjecture under the additional assumption that the domain is h-extendible.
In the second part, we discuss the two core tools used in the proof: the localization of the Bergman kernel for unbounded pseudoconvex domains near a D'Angelo finite type boundary point, and the existence of a weakly pseudoconvex h-extendible boundary point on a bounded real-analytic pseudoconvex domain whose Bergman metric is Kähler–Einstein. These results allow us to reduce the study to the h-extendible case.
The talk is based on joint work with Chin-Yu Hsiao and Xiaojun Huang.
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