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arXiv · 2409.00420

Fully non-linear elliptic equations on compact hyperk\"ahler manifolds

Giovanni Gentili·Luigi Vezzoni
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Abstract

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.

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Giovanni Gentili, Luigi Vezzoni. 2024-08-31. Fully non-linear elliptic equations on compact hyperk\"ahler manifolds. https://arxiv.org/abs/2409.00420

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