Regularity of Solutions to Monge-Ampère Equations on Stein Spaces

Hongyu Chen

Regularity of Solutions to Monge-Ampère Equations on Stein Spaces

Complex Variables 2026-07-08 v1 Analysis of PDEs Differential Geometry

Authors: Hongyu Chen

Abstract

In this note, we study degenerate complex Monge-Amp\`ere equations on singular Stein spaces with right-hand sides depending on the unknown. First, we prove continuity up to the boundary for solutions. Next, under a holomorphic peak-set condition, we prove local H\"older estimates on the regular locus, allowing the boundary datum to fail to be H\"older continuous at the singular boundary. This includes the case of finite singular boundary sets.

Keywords

Monge-Ampere equations Stein spaces regularity Holder estimates degenerate equations boundary behavior

Cite

@article{arxiv.2607.07599,
  title  = {Regularity of Solutions to Monge-Ampère Equations on Stein Spaces},
  author = {Hongyu Chen},
  journal= {arXiv preprint arXiv:2607.07599},
  year   = {2026}
}

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25 pages