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arXiv · 2303.02689

The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds

Lucio Bedulli·Giovanni Gentili·Luigi Vezzoni
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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.

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Lucio Bedulli, Giovanni Gentili, Luigi Vezzoni. 2023-07-14. The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds. https://arxiv.org/abs/2303.02689

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