English

Regularity of solutions to Monge--Amp\`ere equations on compact Hermitian manifolds

Differential Geometry 2026-03-27 v1 Complex Variables

Abstract

We study the stability and H\"older continuity of solutions to degenerate complex Monge--Amp\`ere equations associated with a (non-closed) big form on compact Hermitian manifolds. We also show that the solution is globally continuous when the reference form is the pullback of a Hermitian metric. As a consequence, we establish a uniform diameter bound for the twisted Chern--Ricci flow.

Keywords

Cite

@article{arxiv.2603.25520,
  title  = {Regularity of solutions to Monge--Amp\`ere equations on compact Hermitian manifolds},
  author = {Quang-Tuan Dang},
  journal= {arXiv preprint arXiv:2603.25520},
  year   = {2026}
}

Comments

22 pages. Comments are welcome!