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The complex Monge-Amp\`ere equation with a gradient term

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arxiv 1906.10034 v1 pith:636BWTWK submitted 2019-06-24 math.DG math.APmath.CV

Valentino Tosatti , Ben Weinkove This is my paper · ORCID
classification math.DGmath.APmath.CV
keywords equationcomplexgradientmonge-amptermadditionalcompactconsider
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We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.

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Cited by 2 Pith papers

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  1. 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.

  2. 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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