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Fully non-linear elliptic equations on compact hyperkähler manifolds | Synapse

February 19, 2026Calculus of Variations and Partial Differential Equations0 citationsOpen Access

Fully non-linear elliptic equations on compact hyperkähler manifolds

GGGiovanni Gentili LVLuigi Vezzoni

Key Points

To investigate a class of elliptic equations on hypercomplex manifolds and their solutions' properties.
Analyzed elliptic equations including the quaternionic Monge-Ampère and Hessian equations on hypercomplex manifolds.
Developed a priori estimates for solutions under suitable assumptions.
Proved solutions meet a specific C^{2,α} a priori estimate.
Characterized conditions under which the elliptic equations hold on hyperkähler manifolds.

Abstract

Abstract We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-Ampère equation for quaternionic (n-1) (n - 1) -plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a C^2, C 2, α a priori estimate.

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Cite This Study

Gentili et al. (Tue,) studied this question.

synapsesocial.com/papers/6996a83eecb39a600b3eec93 https://doi.org/https://doi.org/10.1007/s00526-026-03259-8