Stability and H\"older regularity of solutions to complex Monge-Amp\`ere equations on compact Hermitian manifolds

Chinh H. Lu; Trong-Thuc Phung; Tât-Dat Tô

Stability and H\"older regularity of solutions to complex Monge-Amp\`ere equations on compact Hermitian manifolds

Complex Variables 2020-11-17 v2 Analysis of PDEs Differential Geometry

Authors: Chinh H. Lu , Trong-Thuc Phung , Tât-Dat Tô

Abstract

Let $(X,\omega)$ be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge-Amp\`ere equations with right-hand side in $L^p$ , $p>1$ . Using this we prove that the solutions are H\"older continuous with the same exponent as in the K\"ahler case \cite{DDGKPZ14}. Our techniques also apply to the setting of big cohomology classes on compact K\"ahler manifolds.

Keywords

complex Monge-Ampère equation compact Hermitian manifold stability Hölder regularity L^p right-hand side big cohomology class

Cite

@article{arxiv.2003.08417,
  title  = {Stability and H\"older regularity of solutions to complex Monge-Amp\`ere equations on compact Hermitian manifolds},
  author = {Chinh H. Lu and Trong-Thuc Phung and Tât-Dat Tô},
  journal= {arXiv preprint arXiv:2003.08417},
  year   = {2020}
}

Comments

final version to appear in Annales de l'Institut Fourier

Stability and H\"older regularity of solutions to complex Monge-Amp\`ere equations on compact Hermitian manifolds

Abstract

Keywords

Cite

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