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

2019/09/01 by Collins, Tristan C., Picard, Sebastien · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.00447

Abstract

We solve the Dirichlet problem for k-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient scale. The scale allows us to apply a blow-up argument to obtain control on all necessary norms of the solution.

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• Polar sets for m-subharmonic functions on compact Hermitian manifolds
• m-Positivity and Regularisation

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