Scattering theory and inverse scattering theory in hyperbolic space.

发布时间：2025-06-27 作者：浏览次数：

Speaker:	陈露	DateTime:	2025年7月5日（周六）上午10:00-11:00
Brief Introduction to Speaker: 陈露，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。目前研究兴趣主要在几何不等式及其临界点的最优稳定性，各向异性的极小曲面和等周问题，UCP和小性传播以及双曲空间上的反散射问题，在Proc. Lond. Math. Soc.，Analysis & PDE, Adv. Math, Math. Ann., Trans. AMS, Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze，J. Funct. Anal等数学杂志期刊发表论文40余篇。		Place:	国交2号楼315会议室
Abstract: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 and use them to establish the ingoing and outgoing radiation conditions, which are analogues to the Sommerfeld radiation conditions in the Euclidean setting. We also discuss a hyperbolic Rellichs type theorem which guarantees that the scattered field as well as its far-field pattern are uniquely defined. Finally, we introduce the inverse obstacle problem on hyperbolic space. 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.

上一条：这是第一条
下一条： Scalar curvature rigidity of compact manifolds