The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds

2023/03/05 by Lucio Bedulli, Giovanni Gentili, Bedulli, Lucio +3 · 2 citations
Mathematics · Physics and Astronomy · #35K96 #53C26 #53E30 #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2303.02689

openalex publication_date 2023/03/05 · openalex created_date 2023/03/09 · openalex updated_date 2026/07/28

Abstract

We show that the parabolic quaternionic Monge-Ampère equation on a compact hyperkähler manifold has always a long-time solution which once normalized converges smoothly to a solution of the quaternionic Monge-Ampère 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.

Cited by

• A remark on the second order estimates for the quaternionic Calabi-Yau problem on hyperkähler manifolds
• On balanced HKT manifolds

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• Solvability of the quaternionic Monge-Ampere equation on compact\n manifolds with a flat hyperKaehler metric
• A remark on the second order estimates for the quaternionic Calabi-Yau problem on hyperkähler manifolds