The uniformization conjecture in complete non-compact Sasakian manifolds

发布时间：2025-10-24 作者：浏览次数：

Speaker:	韩英波	DateTime:	2025年10月31日(周五) 上午10:30-11:30
Brief Introduction to Speaker: 韩英波，信阳师范大学教授、博士生导师。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月调入信阳师范大学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CR几何分析研究。主持4项国家自然科学基金项目，其中面上项目2项。在国内外重要学术期刊Journal für reine und angewandte Mathematik(Crelle’s Journal)，The Journal of Geometric Analysis, International Mathematical Research Notices，Calculus of Variations and Partial Differential Equations等发表学术论文数十篇。		Place:	国交2号楼315会议室
Abstract:The CR analogue of Yau uniformization conjecture states that any complete noncompact Sasakian manifold of positive CR holomorphic bisectional curvature is CR biholomorphic to the standard Heisenberg group. In this talk, we first 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. Then by using Sasaki-Ricci flow, we affirm the partial result of the above conjecture on Sasakian manifolds. More precisely, we show that a complete noncompact Sasakian manifold of nonnegative and bounded transversal bisectional curature with maximal volume growth is CR biholomorphic to , where is a pseudoconvex domain of .

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