A note on $\tmd$-operator
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909545441263616 |
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| author | Lin, Dexie Zhou, Hengyu |
| author_facet | Lin, Dexie Zhou, Hengyu |
| contents | In almost Kähler manifolds, one of the challenges is to construct an elliptic operator on functions that plays a role analogous to the $\partial\bar{\partial}$ operator in complex or Kähler manifolds. One of the aims of this paper is to revisit the $\tmd$-operator introduced in \cite{TWZZ}. We will provide some local analysis estimates and highlight several difficulties that remain to be addressed. Additionally, we use the Atiyah-Hitchin-Singer operator to demonstrate that every $d$-exact $(1,1)$-form is globally $\tmd$-exact for any compact taming symplectic $4$-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on $\tmd$-operator Lin, Dexie Zhou, Hengyu Differential Geometry In almost Kähler manifolds, one of the challenges is to construct an elliptic operator on functions that plays a role analogous to the $\partial\bar{\partial}$ operator in complex or Kähler manifolds. One of the aims of this paper is to revisit the $\tmd$-operator introduced in \cite{TWZZ}. We will provide some local analysis estimates and highlight several difficulties that remain to be addressed. Additionally, we use the Atiyah-Hitchin-Singer operator to demonstrate that every $d$-exact $(1,1)$-form is globally $\tmd$-exact for any compact taming symplectic $4$-manifold. |
| title | A note on $\tmd$-operator |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.15939 |