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

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

3 Citations (Scopus)

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
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
Publication status	Published - 2 Dec 2020
Externally published	Yes

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10.4310/CAG.2020.V28.N6.A1

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title = "A new geometric flow over K{\"a}hler manifolds",

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",

year = "2020",

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doi = "10.4310/CAG.2020.V28.N6.A1",

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AU - Li, Yi

AU - Yuan, Yuan

AU - Zhang, Yuguang

PY - 2020/12/2

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N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85098323665

U2 - 10.4310/CAG.2020.V28.N6.A1

DO - 10.4310/CAG.2020.V28.N6.A1

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AN - SCOPUS:85098323665

SN - 1019-8385

VL - 28

SP - 1251

EP - 1288

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 6

ER -

A new geometric flow over Kähler manifolds

Abstract

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