A class of the non-degenerate complex quotient equations on compact Kähler manifolds

Zhou, Jundong

doi:10.3934/cpaa.2021085

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2022

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Cited by 3 publications

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“…Later the Eq. (1.3) in Neumann problem, prescribed curvature problem, complex manifolds were also discussed in [4,5,33,7,6,31,32,22].…”

Section: Introductionmentioning

confidence: 98%

The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds

Chen¹,

Xiao²,

Wu³

2022

Preprint

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“…Later the Eq. (1.3) in Neumann problem, prescribed curvature problem, complex manifolds were also discussed in [4,5,33,7,6,31,32,22].…”

Section: Introductionmentioning

confidence: 98%

The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds

Chen¹,

Xiao²,

Wu³

2022

Preprint

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A type of parabolic flow with mixed hessians on compact Kähler manifolds

Tsai

2022

Proc. Amer. Math. Soc.

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We investigate the solvability of a general class of mixed Hessian type equations on compact Kähler manifolds. Based on an observation in Guan and Zhang [Pure Appl. Math. Q. 17 (2021), pp. 865–907], the mixed Hessian equations can be rewritten as elliptic and concave equations which satisfy the general framework in Székelyhidi [J. Differential Geom. 109 (2018), pp. 337–378] and Phong and Tô [Ann. Sci. Éc. Norm. Supér. (4) 54 (2021), pp. 793–829] except one condition. We notice that the absence of this condition can be overcome by using the particular structure of the mixed Hessian equations. As an application, the solvability of the deformed Hermitian Yang-Mills equations in dimension three was also studied.

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Hessian equations of Krylov type on compact Hermitian manifolds

Zhou

Chu

2022

Open Mathematics

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In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix. Under the assumption of the 𝒞-subsolution, we obtain a priori estimates in Γ k − 1 {\Gamma }_{k-1} cone. By using the method of continuity, we prove an existence theorem, which generalizes the relevant results. As an application, we give an alternative way to solve the deformed Hermitian Yang-Mills equation on compact Kähler threefold.

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A class of the non-degenerate complex quotient equations on compact Kähler manifolds

Cited by 3 publications

References 20 publications

The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds

The Dirichlet Problem for mixed Hessian type equations on Riemannian manifolds

A type of parabolic flow with mixed hessians on compact Kähler manifolds

Hessian equations of Krylov type on compact Hermitian manifolds

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