Work

Fully non-linear elliptic equations on compact hyperkähler manifolds

Year: 2026

Type: article

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 $$C^{2,\alpha }$$ C 2 , α a priori estimate.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-026-03259-8

Authors: Giovanni Gentili, Luigi Vezzoni

Institution: University of Turin

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Torino, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni