学术报告

题      目： Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian Manifolds

报  告  人：韩英波   教授  (邀请人：魏国新 )

                               信阳师范学院

时      间：2022-11-25 10:00-11:00

腾 讯 会 议：548-293-290

报告人简介:

       韩英波，博士，教授，2007年7月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数学与统计学院工作至今, 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。主持在研国家自然科学基金面上项目1项，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年获得河南省高校青年骨干教师培养计划，2018年获得河南省优秀教师称号。在国内外重要学术期刊The Journal of Geometric Analysis, International Mathematical Research Notices， Calculus of Variations and Partial Differential Equations， Canadian Journal of Mathematics， Nonlinear Analysis, Science China Mathematics等发表学术论文50余篇。 

摘      要：

       In this talk, we show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative pseudohermitian bisectional curvature with the CR maximal volume growth property. This is the very first step toward the CR analogue of Yau uniformization conjecture which states that any complete noncompact Sasakian manifold of positive pseudohermitian bisectional curvature is CR biholomorphic to the standard Heisenberg group. More precisely, we first construct CR-holomorphic functions with controlled growth in a sequence of exhaustion domains in Sasakian manifolds by applying the Cheeger-Colding theory. Secondly, via the CR analogue of tangent cone at infinity and three circle theorem, we are able to take the subsequence to obtain a nonconstant CR holomorphic function of polynomial growth. This is a joint work with Shu-Cheng Chang, Nan Li and Chien Lin.