应兰州大学数学与统计学院邀请，美国密歇根州立大学Paul Sweeney Jr.博士后将于2025年10月24日（星期五）早晨进行在线学术报告，欢迎广大师生参加。

报告题目：Positive curvature conditions on contractible manifolds

时 间：2025年10月24日（星期五）9:00–10:00

Zoom会议号：859 9751 3043

会议密码：202510

报告摘要：The goal of this talk is to identify curvature conditions that distinguish Euclidean space in the case of open, contractible manifolds and the disk in the case of compact, contractible manifolds with boundary. First, we show that an open manifold that is the interior of a sufficiently connected, compact, contractible 5-manifold with boundary and supports a complete Riemannian metric with uniformly positive scalar curvature is diffeomorphic to Euclidean 5-space. Next, we investigate the analogous question for compact manifolds with boundary: Must a compact, contractible manifold that supports a Riemannian metric with positive scalar curvature and mean convex boundary necessarily be the disk? We present examples demonstrating that this curvature condition alone cannot distinguish the disk; on the other hand, we exhibit stronger curvature conditions that allow us to draw such a conclusion.

报告人简介

Paul Sweeney Jr.，美国密歇根州立大学博士后。他于2024年在美国纽约州立大学石溪分校数学系取得博士学位，曾在意大利特伦托大学(University of Trento)做博士后研究。Paul Sweeney Jr.博士的研究兴趣为：几何分析，广义相对论，几何测度论，数量曲率和流形的收敛。

甘肃应用数学中心

数学与统计学院

萃英学院

2025年10月22日