学术报告
报告题目:On CR analogue of Yau's conjecture, the CR Poincare-Lelong equation and their applications
报告人:韩英波副教授(信阳师范学院)
报告时间:2018年4月2日下午3:00
报告地点:25教学楼14楼报告厅
参加人员:教师、研究生、本科生
摘要:In this talk, we first derive the CR volume doubling property, CR Sobolev inequality, and mean value inequality. We then apply them to prove the CR analogue of Yau's conjecture on the space consisting of all pseudoharmonic functions of polynomial growth of degree at most d in a complete noncompact pseudohermitian (2n+1)-manifold. Secondly we solve the so-called CR Poincare Lelong equation by solving the CR Poisson equation on a complete noncompact CR (2n+1)-manifold with nonnegative pseudohermitian bisectional curvature tensors and vanishing torsion which is an odd dimensional counterpart of Keahler geometry. With its applications plus the CR Liouville property, we study the structures of complete noncompact Sasakian manifolds.
个人简介:韩英波,博士,副教授,硕士生导师,2002年于曲阜师范大学数学系获理学学士学位,2007年于复旦大学数学科学学院获理学博士学位,2007.07-2009.12于东南大学数学系工作,2009年12月调入信阳师范学院星际电子在线工作至今, 2016.12-2017.12于美国俄克拉荷马大学数学系学术访问。主要从事微分几何研究。主持完成2项国家自然科学基金项目。2015年获得河南省教育厅学术与技术带头人称号,2016年获河南省高校青年骨干教师培养计划。在国内外重要学术期刊Nonlinear Analysis、Journal of Mathematical Analysis and Applications、Journal of Geometry and Physics、Results in Math、Science China Mathematics等发表学术论文40余篇。