The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds
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| Názov: | The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds |
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| Autori: | Fu, Jixiang, Xu, Xin, Zhang, Dekai |
| Zdroj: | Chinese Annals of Mathematics, Series B. 46:647-662 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Springer Science and Business Media LLC, 2025. |
| Rok vydania: | 2025 |
| Predmety: | 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) |
| Popis: | 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. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1860-6261 0252-9599 |
| DOI: | 10.1007/s11401-025-0033-0 |
| DOI: | 10.48550/arxiv.2310.09225 |
| Prístupová URL adresa: | http://arxiv.org/abs/2310.09225 |
| Rights: | Springer Nature TDM CC BY NC SA |
| Prístupové číslo: | edsair.doi.dedup.....a1d344a63c40fc0193ed57f25290ad1c |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | 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. |
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| ISSN: | 18606261 02529599 |
| DOI: | 10.1007/s11401-025-0033-0 |