The Monge-Ampère equation for (n-1)-quaternionic PSH functions on a hyperKähler manifold

2023/01/22 by Jixiang Fu, Xin Xu, Fu, Jixiang +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2301.09119

openalex publication_date 2023/01/22 · openalex created_date 2023/01/25 · openalex updated_date 2026/07/28

Abstract

We prove the existence of unique smooth solutions to the quaternionic Monge-Ampère equation for (n-1)-quaternionic plurisubharmonic functions on a hyperKähler manifold and thus obtain solutions for the quaternionic form type equation. We derive C⁰ estimate by establishing a Cherrier-type inequality as in Tosatti and Weinkove [22]. By adopting the approach of Dinew and Sroka [9] to our context, we obtain C¹ and C² estimates without assuming the flatness of underlying hyperKähler metric comparing to previous results [14].

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