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The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds

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arxiv 1905.02412 v4 pith:BN4WHGLI submitted 2019-05-07 math.DG

Ke Feng , Huabin Ge , Tao Zheng This is my paper · ORCID
classification math.DG
keywords equationsmanifoldsdirichlethermitianproblemadmissibleestimatesfully
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abstract

We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the gradients of the solutions. In some special cases, we obtain the gradient estimates, and hence we can solve the corresponding Dirichlet problem with admissible subsolutions. We also study the Hessian quotient equations and $(m-1,m-1)$-Hessian quotient equations on compact Hermitian manifolds without boundary.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Dirichlet Problem for the $k$-Hessian Equation on a complex manifold

    math.DG 2019-09 accept novelty 8.0 of 10

    The Dirichlet problem for complex k-Hessian equations on compact Hermitian manifolds with boundary is solved under the assumption that a smooth subsolution exists.

  2. Second order estimates for $\chi$-semi convex solutions of Hessian equations on Hermitian manifolds

    math.AP 2025-01 conditional novelty 6.0 of 10

    For admissible, chi-semi-convex solutions of complex Hessian equations with gradient terms on compact Hermitian manifolds, the paper proves uniform second-order estimates.

  3. Second order estimates for complex Hessian equations on Hermitian manifolds

    math.AP 2019-08 conditional novelty 6.0 of 10

    For chi-plurisubharmonic solutions of complex Hessian equations with gradient-dependent right-hand sides on compact Hermitian manifolds, the second covariant derivative of the solution is uniformly bounded in terms of...

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