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 (2023) prove the conjecture of Alesker and Verbitsky (2010). We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.
The parabolic quaternionic Calabi–Yau equation on hyperkähler manifolds
Bedulli, Lucio;Vezzoni, Luigi
2024-01-01
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 (2023) prove the conjecture of Alesker and Verbitsky (2010). We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.File in questo prodotto:
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