On the tangent cone of Kähler manifolds with Ricci curvature lower bound

The Kähler - Ricci flow on Kähler manifolds with 2 traceless bisectional curvature operator

Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

We prove a new kind of estimate that holds on any manifold with a lower Ricci bound. It relates the geometry of two small balls with the same radius, potentially far apart, but centered in the interior of a common minimizing geodesic. It reveals new, previously unknown, properties that all generalized spaces with a lower Ricci curvature bound must have and it has a number of applications. This ...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

Lower Bound Estimate for the First Eigenvalue of Compact Manifolds with Negative Lower Bound of Ricci Curvature

We estimate the lower bound of the first non-zero eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang.

0 Ricci flow on Kähler manifolds