English

The parabolic quaternionic Monge-Amp\`{e}re type equation on hyperK\"{a}hler manifolds

Differential Geometry 2023-10-16 v1 Analysis of PDEs Complex Variables

Abstract

We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Amp\`{e}re type equation on a compact hyperK\"{a}hler manifold. We also show that after normalization, the solution converges smoothly to the unique solution of the Monge-Amp\`{e}re equation for (n1)(n-1)-quaternionic psh functions.

Keywords

Cite

@article{arxiv.2310.09225,
  title  = {The parabolic quaternionic Monge-Amp\`{e}re type equation on hyperK\"{a}hler manifolds},
  author = {Jixiang Fu and Xin Xu and Dekai Zhang},
  journal= {arXiv preprint arXiv:2310.09225},
  year   = {2023}
}
R2 v1 2026-06-28T12:50:03.873Z