The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

Jixiang Fu; Xin Xu; Dekai Zhang

doi:10.1007/s11401-025-0033-0

The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

Jixiang Fu
, Xin Xu
, Dekai Zhang^*

^*Corresponding author for this work

School of Mathematical Sciences

Fudan University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for (n − 1)-quaternionic psh functions.

Original language	English
Pages (from-to)	647-662
Number of pages	16
Journal	Chinese Annals of Mathematics. Series B
Volume	46
Issue number	5
DOIs	https://doi.org/10.1007/s11401-025-0033-0
State	Published - Sep 2025

Keywords

32W20
53C26
58J35
HyperKähler manifold
Parabolic equation
Quaternionic Monge-Ampère type equation

Access to Document

10.1007/s11401-025-0033-0

Cite this

@article{50e3e5ce2ab242e3aa2adc2f4d29066f,

title = "The Parabolic Quaternionic Monge-Amp{\`e}re Type Equation on HyperK{\"a}hler Manifolds",

abstract = "This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Amp{\`e}re type equation on compact hyperK{\"a}hler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Amp{\`e}re equation for (n − 1)-quaternionic psh functions.",

keywords = "32W20, 53C26, 58J35, HyperK{\"a}hler manifold, Parabolic equation, Quaternionic Monge-Amp{\`e}re type equation",

author = "Jixiang Fu and Xin Xu and Dekai Zhang",

note = "Publisher Copyright: {\textcopyright} The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2025.",

year = "2025",

month = sep,

doi = "10.1007/s11401-025-0033-0",

language = "英语",

volume = "46",

pages = "647--662",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

publisher = "Springer Verlag",

number = "5",

}

TY - JOUR

T1 - The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

AU - Fu, Jixiang

AU - Xu, Xin

AU - Zhang, Dekai

N1 - Publisher Copyright: © The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2025.

PY - 2025/9

Y1 - 2025/9

N2 - This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for (n − 1)-quaternionic psh functions.

AB - This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for (n − 1)-quaternionic psh functions.

KW - 32W20

KW - 53C26

KW - 58J35

KW - HyperKähler manifold

KW - Parabolic equation

KW - Quaternionic Monge-Ampère type equation

UR - https://www.scopus.com/pages/publications/105015063122

U2 - 10.1007/s11401-025-0033-0

DO - 10.1007/s11401-025-0033-0

M3 - 文章

AN - SCOPUS:105015063122

SN - 0252-9599

VL - 46

SP - 647

EP - 662

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 5

ER -

The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this