JournalsrmiVol. 40, No. 6pp. 2291–2310

The parabolic quaternionic Calabi–Yau equation on hyperkähler manifolds

  • Lucio Bedulli

    Università dell’Aquila, L’Aquila, Italy

  • Giovanni Gentili

    Università degli Studi di Firenze, Firenze, Italy; Università degli Studi di Torino, Torino, Italy

  • Luigi Vezzoni

    Università degli Studi di Torino, Torino, Italy
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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 (2023) prove the conjecture of Alesker and Verbitsky (2010). We also introduce an analogue of the Chern–Ricci flow in hyperhermitian manifolds.

Cite this article

Lucio Bedulli, Giovanni Gentili, Luigi Vezzoni, The parabolic quaternionic Calabi–Yau equation on hyperkähler manifolds. Rev. Mat. Iberoam. 40 (2024), no. 6, pp. 2291–2310

DOI 10.4171/RMI/1499