Fully non-linear elliptic equations on compact hyperkähler manifolds

2024/08/31 by Gentili, Giovanni, Vezzoni, Luigi
#32W50 #35B45 #35J60 #53C26 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.00420

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)-plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a C^2,α a priori estimate.

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