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 -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}
}