Volume-Preserving Mean Curvature Flow with Capillary Boundary in Hyperbolic Space

发布时间：2025-09-09 作者：浏览次数：

Speaker:	陈怡敏	DateTime:	2025年9月13日（周六）上午11:00-12:00
Brief Introduction to Speaker: 陈怡敏（韩国釜山国立大学），2022年博士毕业于清华大学数学系，2022年-2025年在韩国釜山国立大学从事博士后研究员的工作。完成一项韩国国家基金会的青年基金项目。主要研究方向是毛细管超曲面的刚性和相关的曲率流问题。		Place:	国交2号楼201会议室
Abstract:We study capillary hypersurfaces in hyperbolic space that meet a totally geodesic hyperplane at a fixed angle. A constrained mean curvature flow is introduced which exactly preserves the enclosed volume while strictly decreasing a energy functional. First, we prove global existence and convergence of the flow. Next, we show that as time goes to infinity the evolving hypersurfaces converge smoothly to a totally umbilical “cap” with the same contact angle. Finally, we demonstrate that this cap uniquely minimizes the energy among all hypersurfaces enclosing the same volume.