English

Weak solutions of complex Hessian equations on compact Hermitian manifolds

Complex Variables 2019-02-20 v2 Differential Geometry

Abstract

We prove the existence of weak solutions of complex mm-Hessian equations on compact Hermitian manifolds for the nonnegative right hand side belonging to Lp,p>n/mL^p, p>n/m (nn 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.

Keywords

Cite

@article{arxiv.1507.06755,
  title  = {Weak solutions of complex Hessian equations on compact Hermitian manifolds},
  author = {Slawomir Kolodziej and Ngoc Cuong Nguyen},
  journal= {arXiv preprint arXiv:1507.06755},
  year   = {2019}
}

Comments

27 pages, accepted by Compos. Math