On the finite energy classes of quaternionic plurisubharmonic functions

2023/10/24 by Thai Duong, Do, Thai Duong, Van Thien Nguyen +1
Mathematics · Physics and Astronomy · #31C10 #32U15 #32U40 #Black Holes and Theoretical Physics #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2310.15453

openalex publication_date 2023/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the finite p-energy classes E_p of quaternionic plurisubharmonic functions of Cegrell type. We also construct an example to show that the optimal constant in the energy estimate is strictly bigger than 1 for p>0, p≠ 1. This leads us to the fact that we can not use the variational method to solve the quaternionic Monge-Ampère equation for the classes E_p when p>0, p≠ 1.

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