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arXiv · 1909.00447

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

Tristan C. Collins·Sebastien Picard
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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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Tristan C. Collins, Sebastien Picard. 2019-09-01. The Dirichlet Problem for the $k$-Hessian Equation on a complex manifold. https://arxiv.org/abs/1909.00447

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