Parabolic Flow for Generalized complex Monge-Amp\`ere type equations

Wei Sun

Parabolic Flow for Generalized complex Monge-Amp\`ere type equations

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arxiv 1501.04255 v1 pith:63ODQ4XA submitted 2015-01-18 math.DG math.AP

Wei Sun This is my paper · ORCID

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keywords complexequationsflowgeneralizedinftymonge-ampparabolictype

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abstract

We study the parabolic flow for generalized complex Monge-Amp\`ere type equations on closed Hermitian manifolds. We derive {\em a priori} $C^\infty$ estimates for normalized solutions, and then prove the $C^\infty$ convergence.

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Weak solutions of the generalized Monge-Amp\`ere equation and the supercritical deformed Hermitian-Yang-Mills equation: boundary cases
math.DG 2026-05 unverdicted novelty 5.0 of 10

Proves existence, uniqueness and flow convergence for weak solutions of generalized Monge-Ampère and supercritical dHYM equations on boundary cohomology classes via viscosity and pluripotential techniques.

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