Diameter estimates in Kähler geometry II: removing the small degeneracy assumption

TY - JOUR

T1 - Diameter estimates in Kähler geometry II

T2 - removing the small degeneracy assumption

AU - Guo, Bin

AU - Phong, Duong H.

AU - Song, Jian

AU - Sturm, Jacob

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2024/11

Y1 - 2024/11

N2 - 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.

AB - 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.

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U2 - 10.1007/s00209-024-03600-x

DO - 10.1007/s00209-024-03600-x

M3 - Article

SN - 0025-5874

VL - 308

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

M1 - 43

ER -