The parabolic quaternionic Calabi-Yau equation on hyperk\"ahler manifolds
Differential Geometry
2023-07-17 v3
Abstract
We show that the parabolic quaternionic Monge-Amp\`ere equation on a compact hyperk\"ahler manifold has always a long-time solution which once normalized converges smoothly to a solution of the quaternionic Monge-Amp\`ere equation. This is the same setting in which Dinew and Sroka prove the conjecture of Alesker and Verbitsky. We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.
Keywords
Cite
@article{arxiv.2303.02689,
title = {The parabolic quaternionic Calabi-Yau equation on hyperk\"ahler manifolds},
author = {Lucio Bedulli and Giovanni Gentili and Luigi Vezzoni},
journal= {arXiv preprint arXiv:2303.02689},
year = {2023}
}
Comments
This is a new version of the paper "The Calabi-Yau theorem on Hypercomplex manifolds", which was withdrawn due to a crucial mistake in a key Lemma. In this new version we fix the mistake by introducing the extra assumption of the existence of a background hyperk\"ahler metric