#### Vol. 14, No. 7, 2021

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Some refinements of the partial $C^0$ estimate

### Kewei Zhang

Vol. 14 (2021), No. 7, 2307–2326
##### Abstract

Relying on the recent work of Liu and 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.

##### Keywords
Bergman kernel, partial $C^0$ estimate, Kähler–Ricci flow
##### Mathematical Subject Classification 2010
Primary: 32A25, 53C44