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arXiv · 1507.06755

Weak solutions of complex Hessian equations on compact Hermitian manifolds

Slawomir Kolodziej·Ngoc Cuong Nguyen
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Abstract

We prove the existence of weak solutions of complex $m-$Hessian equations on compact Hermitian manifolds for the nonnegative right hand side belonging to $L^p, p>n/m$ ($n$ is the dimension of the manifold). For smooth, positive data the equation has been recently solved by Szekelyhidi and Zhang. We also give a stability result for such solutions.

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Slawomir Kolodziej, Ngoc Cuong Nguyen. 2015-07-24. Weak solutions of complex Hessian equations on compact Hermitian manifolds. https://doi.org/10.1112/s0010437x16007417

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