A new geometric flow over Kähler manifolds

Yi Li; Yuan Yuan; Yuguang Zhang

doi:10.4310/CAG.2020.V28.N6.A1

A new geometric flow over Kähler manifolds

Yi Li, Yuan Yuan, Yuguang Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, we introduce a geometric flow for Kähler metrics ω_t coupled with closed (1, 1)-forms α_t on a compact Kähler manifold, whose stationary solution is a constant scalar curvature Kähler (cscK) metric, coupled with a harmonic (1, 1)-form. We establish the long-time existence, i.e., assuming the initial (1, 1)-form α is nonnegative, then the flow exists as long as the norm of the Riemannian curvature tensors are bounded.

Original language	English (US)
Pages (from-to)	1251-1288
Number of pages	38
Journal	Communications in Analysis and Geometry
Volume	28
Issue number	6
DOIs	https://doi.org/10.4310/CAG.2020.V28.N6.A1
State	Published - Dec 2 2020

ASJC Scopus subject areas

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

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10.4310/CAG.2020.V28.N6.A1

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abstract = "In this paper, we introduce a geometric flow for K{\"a}hler metrics ωt coupled with closed (1, 1)-forms αt on a compact K{\"a}hler manifold, whose stationary solution is a constant scalar curvature K{\"a}hler (cscK) metric, coupled with a harmonic (1, 1)-form. We establish the long-time existence, i.e., assuming the initial (1, 1)-form α is nonnegative, then the flow exists as long as the norm of the Riemannian curvature tensors are bounded.",

author = "Yi Li and Yuan Yuan and Yuguang Zhang",

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AU - Zhang, Yuguang

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AB - In this paper, we introduce a geometric flow for Kähler metrics ωt coupled with closed (1, 1)-forms αt on a compact Kähler manifold, whose stationary solution is a constant scalar curvature Kähler (cscK) metric, coupled with a harmonic (1, 1)-form. We establish the long-time existence, i.e., assuming the initial (1, 1)-form α is nonnegative, then the flow exists as long as the norm of the Riemannian curvature tensors are bounded.

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ER -

A new geometric flow over Kähler manifolds

Abstract

ASJC Scopus subject areas

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