A parabolic approach to the Calabi-Yau problem in HKT geometry
Differential Geometry
2021-12-22 v2
Abstract
We consider the natural generalization of the parabolic Monge-Amp\`ere equation to HKT geometry. We prove that in the compact case the equation has always a short-time solution and when the hypercomplex manifold is locally flat and admits a hyperk\"ahler metric, then the equation has a long-time solution whose normalization converges to a solution of the quaternionic Monge-Amp\`ere equation introduced by Alesker and Verbitsky. The result gives an alternative proof of a theorem of Alesker.
Keywords
Cite
@article{arxiv.2105.04925,
title = {A parabolic approach to the Calabi-Yau problem in HKT geometry},
author = {Lucio Bedulli and Giovanni Gentili and Luigi Vezzoni},
journal= {arXiv preprint arXiv:2105.04925},
year = {2021}
}
Comments
15 pages. Revisited version. To appear in Math. Z