Yau Uniformization Conjecture on Complete Noncompact Sasakian Manifolds

  [NTNU MATH-CAG-MSRC Joint Program on Geometric Analysis] 【09月27日】張樹城 / Topics on Geometry and Analysis of Sasakian Five-Manifolds: Lecture Three

Time  :  15:30-17:00 (Wednesday), 09/27, 2023
Place :    M210, Math. Dept., National Taiwan Normal University

In this lecture series, we will address the related issues on Sasakian geometry including :

     (I) Lecture One : Geometrization Problems in Sasakian 5-Manifolds (9/13)
     (II) Lecture Two : Foliation Minimal Model Program on Sasakian Five-Manifolds (9/20)
     (III) Lecture Three : Topology and Geometry of Legendrian Submanifolds of Sasakian Manifolds (9/27)
     (IV) Lecture Four : Yau Uniformization Conjecture on Complete Noncompact Sasakian Manifolds (10/4)

Lecture Three  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. The first key step is to show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative CR holomorphic bisectional curvature with the CR maximal volume growth property which is due to Chang-Han-Li-Lin. In this lecture, among the others, we will address this issue via the the Sasaki-Ricci flow.