January 21, 2022
Some new rigidity results in Kähler geometry
I will discuss two new results in rigidity Kähler geometry. I will first talk about the (almost) rigidity of Kähler manifolds with positive Ricci curvature and almost maximal volume. I will then discuss the rigidity of Kähler manifolds with positive bi-sectional curvature and maximal diameter. The first result is a complex analogue of a famous volume rigidity theorem of Colding, and the second result is of course the complex analogue of the well-known maximal diameter theorem of Cheng. This is joint work with Harish Seshadri and Jian Song.