The parabolic quaternionic Calabi-Yau equation on hyperk\'ahler manifolds

Autor:	Bedulli, Lucio, Gentili, Giovanni, Vezzoni, Luigi
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry 53C26 35K96 53E30
Druh dokumentu:	Working Paper
Popis:	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. Comment: This is a new version of the paper "The Calabi-Yau theorem on Hypercomplex manifolds", which was withdrawn due to a crucial mistake in a key Lemma.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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.02689 Zobrazit plný text záznamu View this record from Arxiv