报告时间：2024年12月27日（星期五）10:00-11:00

报告地点：理学楼609报告厅

报告题目：A scattering theory on hyperbolic spaces

报告摘要: In this talk, we introduce a theoretical framework for time-harmonic wave

scattering on hyperbolic spaces. Using the limiting absorption principle (LAP), we derive the explicit forms of the ingoing and outgoing Green functions of the Helmholtz operator of hyperbolic spaces. Then we give the accurate characterisations of the asymptotic behaviours of the Green functions and use them to establish the ingoing and outgoing radiation conditions, which are analogues to the Sommerfeld radiation conditions in the Euclidean setting. Finally, we also discuss a hyperbolic Rellichs type theorem which guarantees that the scattered field as well as its far-field pattern are uniquely defined. To our best knowledge, the theoretical framework is new to the literature and it paves the way for many subsequent developments for wave scattering on hyperbolic spaces. This talk is based on the joint work with Professor Hongyu Liu from City University of Hong Kong.

报告人简介：北京理工大学长聘副教授，博导，小米青年学者。2018年博士毕业于北京师范大学，主持国家自然科学基金青年项目和面上项目各一项，参与一项国家重点研发青年科学家项目, 研究方向为非线性泛函分析和几何不等式。在几何不等式的最优常数和稳定性，指数增长的薛定谔方程的量化分析，双曲空间上的散色理论等方面取得了重要进展，在Proc. Lond. Math. Soc.， Adv. Math,  Trans. AMS,  Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze、J. Funct. Anal等国际一流杂志期刊上发表论文40余篇.