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Title: Diameter estimates in K\"ahler geometry
Diameter estimates for K\"ahler metrics are established 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-Amp\`ere equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time existence of the K\"ahler-Ricci flow and finite-time solutions when the K\"ahler class is big, as well as for special vibrations of Calabi-Yau manifolds.  more » « less
Award ID(s):
2203273
PAR ID:
10542014
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Wiley
Date Published:
Journal Name:
Communications on pure and applied mathematics
ISSN:
0010-3640
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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