Diameter estimates in Kähler geometry
type: Item
instance of: scholarly article
title: Diameter estimates in Kähler geometry
zbMATH Open document ID: 1547.53083
author: Bin Guo
author: D. H. Phong
author: Jian Song
author: Jacob Sturm
published in: Communications on Pure and Applied Mathematics
publication date: 2024-08-14T00:00:00Z
review text: The authors establish diameter estimates for Kähler metrics which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for \(L_\infty\) estimates for the Monge-Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, they solve the long-standing problem of uniform diameter bounds and Gromov-Hausdorff convergence of the Kähler-Ricci flow, for both finite-time and long-time solutions.
reviewed by: Nikolay Gusevskii
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53E30
Mathematics Subject Classification ID: 32W20
zbMATH DE Number: 7896925
zbMATH Keywords: entropy
zbMATH Keywords: Kähler-Ricci flow
zbMATH Keywords: Monge-Ampère equation
MaRDI profile type: Publication
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DOI: 10.1002/CPA.22196
description: scientific article; zbMATH DE number 7896925