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Fully Non-linear Elliptic Equations on Compact Hyperk\"ahler Manifolds by Gentili, Giovanni; Vezzoni, Luigi is a scholarly article available to read on EtoBox.

What is Fully Non-linear Elliptic Equations on Compact Hyperk\"ahler Manifolds about?

We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Amp\`ere equation, the quaternionic Hessian equation and the Monge-Amp\`ere equation for quaternionic $(n-1)$-plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperk\"ahler manifolds satisfy a $C^{2,\alpha}$ a priori estimate.

Author

Gentili, Giovanni; Vezzoni, Luigi

Published

2024

Language

EN