Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2019
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912082506547200 |
|---|---|
| author | Chiu, Shih-Kai |
| author_facet | Chiu, Shih-Kai |
| contents | On a complete Calabi-Yau manifold $M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville type theorem for harmonic $1$-forms, which follows from a new local $L^2$ estimate of the exterior derivative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_12965 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth Chiu, Shih-Kai Differential Geometry On a complete Calabi-Yau manifold $M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon-Hein. We prove this result by proving a Liouville type theorem for harmonic $1$-forms, which follows from a new local $L^2$ estimate of the exterior derivative. |
| title | Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1905.12965 |