2023/10/19 by Zhang Jiaogen, Zhang, Jiaogen
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2310.12597
openalex publication_date 2023/10/19 · openalex created_date 2023/10/21 · openalex updated_date 2026/07/28
The quaternionic Calabi conjecture, posed by Alesker and Verbitsky \citeAlesker-Verbitsky (2010), predicts that the quaternionic Monge-Ampère equation can always be solved on any compact HKT manifold. Motivated by this conjecture, we will introduce a quaternionic version of the Gauduchon conjecture on any compact SL(n,ℍ)-manifold, specifically addressing the existence of quaternionic Gauduchon metrics with prescribed volume form. We reframe this question as a special case of fully nonlinear elliptic equations of second order and subsequently establish a uniform estimate for the potential function.