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
几何分析研讨班
Speaker: 杨博 博士后（清华大学）
Inviter: 杨明轩
Language: Chinese
Title: Existence and nonexistence results for a nonlocal isoperimetric problem on $\mathbb{H}^n$
Time & Venue: 2026年6月22日16:00-17:00 & ZoomID：373-477-819
Abstract: In this talk, I will discuss a nonlocal isoperimetric problem in hyperbolic space, where the energy functional consists of the perimeter and a nonlocal interaction term involving a negative power of the hyperbolic distance. Motivated by the extensively studied Euclidean case, we investigate how the negative curvature of the ambient space influences the existence and shape of minimizers. I will present our main results: for sufficiently small prescribed volume, geodesic balls are the unique minimizers up to hyperbolic isometries, while for large volumes, minimizers do not exist under certain ranges of the exponent in the nonlocal term. This talk highlights the interplay between perimeter, nonlocal interactions, and the geometry of hyperbolic space. This is a joint work with Prof. Haizhong Li.
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