English

Fully non-linear elliptic equations on noncompact complex manifolds

Differential Geometry 2025-12-24 v2 Analysis of PDEs

Abstract

In this paper, we establish a priori estimates and existence results for solutions of a general class of fully non-linear equations on noncompact K\"{a}hler and Hermitian manifolds. As geometric applications, we construct complete K\"{a}hler metrics with prescribed volume forms on strictly pseudoconvex domains, as well as find Einstein metrics on complete noncompact K\"{a}hler manifolds and Hessian manifolds with negative first Chern class.

Keywords

Cite

@article{arxiv.2512.15350,
  title  = {Fully non-linear elliptic equations on noncompact complex manifolds},
  author = {Hanzhang Yin},
  journal= {arXiv preprint arXiv:2512.15350},
  year   = {2025}
}
R2 v1 2026-07-01T08:29:01.044Z