The complex Hessian quotient flow on compact Hermitian manifolds

Jundong Zhou; Yawei Chu; Jundong Zhou; Yawei Chu

doi:10.3934/math.2022416

AIMS Mathematics

2022, Volume 7, Issue 5: 7441-7461. doi: 10.3934/math.2022416

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Research article

The complex Hessian quotient flow on compact Hermitian manifolds

Jundong Zhou ^,,
Yawei Chu

School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China

Received: 22 August 2021 Accepted: 09 February 2022 Published: 14 February 2022
MSC : 53C55, 58J05, 58J35

In this paper, we consider the parabolic Hessian quotient equation on compact Hermitian manifolds. By setting up a priori estimates of the admissible solutions, we prove the long-time existence of the solution to the parabolic Hessian quotient equation and its convergence. As an application, we show the solvability of a class of complex Hessian quotient equations, which generalizes the relevant results.
- Hermitian manifolds,
- complex quotient flow,
- a priori estimates,
- long-time existence,
- convergence
Citation: Jundong Zhou, Yawei Chu. The complex Hessian quotient flow on compact Hermitian manifolds[J]. AIMS Mathematics, 2022, 7(5): 7441-7461. doi: 10.3934/math.2022416

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Abstract

In this paper, we consider the parabolic Hessian quotient equation on compact Hermitian manifolds. By setting up a priori estimates of the admissible solutions, we prove the long-time existence of the solution to the parabolic Hessian quotient equation and its convergence. As an application, we show the solvability of a class of complex Hessian quotient equations, which generalizes the relevant results.

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