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Diameter estimates in K\"ahler geometry II: removing the small degeneracy assumption

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arxiv 2405.18280 v1 pith:CICASU6P submitted 2024-05-28 math.DG math.APmath.CV

Bin Guo , Duong H. Phong , Jian Song , Jacob Sturm This is my paper · ORCID
classification math.DGmath.APmath.CV
keywords assumptiondegeneracysmallahlerdiameterestimatesachievedbound
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In this short note, we remove the small degeneracy assumption in our earlier works [10, 11]. This is achieved by a technical improvement of Corollary 5.1 in [10]. As a consequence, we establish the same geometric estimates for diameter, Green's functions and Sobolev inequalities under an entropy bound for the K\"ahler metrics, without any small degeneracy assumption.

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