English

Modulus of Continuity of Solutions to Complex Monge-Amp\`ere Equations on Stein Spaces

Complex Variables 2026-01-22 v3 Analysis of PDEs Differential Geometry

Abstract

In this paper, we study the modulus of continuity of solutions to Dirichlet problems for complex Monge-Amp\`ere equations with LpL^p densities on Stein spaces with isolated singularities. In particular, we prove such solutions are H\"older continuous outside singular points if the boundary data is H\"older continuous.

Keywords

Cite

@article{arxiv.2405.17242,
  title  = {Modulus of Continuity of Solutions to Complex Monge-Amp\`ere Equations on Stein Spaces},
  author = {Guilherme Cerqueira-Gonçalves},
  journal= {arXiv preprint arXiv:2405.17242},
  year   = {2026}
}

Comments

14 pages. Final version to appear in IUMJ