Name: The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds
Keywords: Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Mathematics - Complex Variables, FOS: Mathematics, Complex Variables (math.CV), Analysis of PDEs (math.AP)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2025Embargo end date: 01 Jan 2023 English Publisher:Springer Science and Business Media LLCJournal:Chinese Annals of Mathematics, Series B, volume 46, pages 647-662 (issn: 0252-9599, eissn: 1860-6261,

Authors: Fu, Jixiang; Xu, Xin; Zhang, Dekai;

doi: 10.1007/s11401-025-0033-0 , 10.48550/arxiv.2310.09225

arXiv: http://arxiv.org/abs/2310.09225

The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

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Abstract

We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Ampère type equation on a compact hyperKähler manifold. We also show that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for $(n-1)$-quaternionic psh functions.

Keywords

Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Mathematics - Complex Variables, FOS: Mathematics, Complex Variables (math.CV), Analysis of PDEs (math.AP)

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