动力系统学术报告

题目：On the the Dirichlet Problem at Infinity and Poisson Boundary beyond Non-positive Curvature

报告人：刘飞 副教授（山东科技大学）

摘要：In this talk, we will investigate the problem of the existence of the bounded harmonic functions on a simply connected Riemannian manifold M without conjugate points, which can be compactified via the ideal boundary ∂M. If M is a uniform visibility manifold without conjugate points which satisfies the Axiom 2, or M is a rank 1 manifold without focal points, we show that for a given continuous function on ∂M, there exists a harmonic extension to M. And moreover, the Brownian motions defines a family of harmonic measures  on ∂M, we show that (∂M, ) is isomorphic to the Poisson boundary of M. This is a joint work with Yinghan Zhang, based on our previous research on the dynamics and geometry of the manifolds beyond non-positive curvature.

报告时间：2025年8月18日（星期一）上午11:00--12:00

报告地点：教二楼613

联系人：王方