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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2310.12597 |
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| _version_ | 1866929425083269120 |
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| author | Zhang, Jiaogen |
| author_facet | Zhang, Jiaogen |
| contents | The quaternionic Calabi conjecture, posed by Alesker and Verbitsky \cite{Alesker-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 $SL(n,\mathbb{H})$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12597 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^\infty$ estimate for the potential of quaternionic Gauduchon metric with prescribed volume form Zhang, Jiaogen Differential Geometry Analysis of PDEs The quaternionic Calabi conjecture, posed by Alesker and Verbitsky \cite{Alesker-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 $SL(n,\mathbb{H})$-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. |
| title | $L^\infty$ estimate for the potential of quaternionic Gauduchon metric with prescribed volume form |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2310.12597 |