Some refinements of the partial $C^0$ estimate

Abstract

Relying on the recent work of Liu-Székelyhidi we give a weak asymptotic estimate for the Bergman kernels of polarized Kähler manifolds with Ricci lower bound and Sobolev constant upper bound. We will also give a simple proof for the partial $C^0$ estimate along the (generalized) Kähler-Ricci flow on Fano manifolds.

Comments are welcome!

References in corpus (2)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• Compactness of Kahler-Ricci solitons on Fano manifolds

Cited by in corpus (1)

• An explicit estimate of the Bergman kernel for positive line bundles