Diameter estimates in Kähler geometry II: removing the small degeneracy assumption
摘要
In this short note, we remove the small degeneracy assumption in our earlier works (Guo et al. in Diameter estimates in Kähler geometry. Commun Pure Appl Math. arXiv:2209.09428; Sobolev inequalities on Kähler spaces. arXiv:2311.00221). This is achieved by a technical improvement of Corollary 5.1 in Guo et al. As a consequence, we establish the same geometric estimates for diameter, Green’s functions and Sobolev inequalities under an entropy bound for the Kähler metrics, without any small degeneracy assumption.