A potential theory for the Wess--Zumino--Witten equation in the space of Kähler potentials
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912610168864768 |
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| author | Wu, Kuang-Ru |
| author_facet | Wu, Kuang-Ru |
| contents | We develop a potential theory for the Wess--Zumino--Witten (WZW) equation in the space of Kähler potentials which is parallel to the potential theory for the Hermitian--Yang--Mills equation. A concept called $ω$-harmonicity on graphs is introduced which characterizes the WZW equation. We also show that, with respect to a Banach--Mazur type distance function, the distance between two solutions of the WZW equation is subharmonic.
The harmonic map into the space of Kähler potentials, as a special case of the WZW equation, is also investigated. In particular, we show the solvability of the Dirichlet problem for the harmonic map, and the approximation/quantization by its finite dimensional counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00710 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A potential theory for the Wess--Zumino--Witten equation in the space of Kähler potentials Wu, Kuang-Ru Differential Geometry 32Q15, 32U05 We develop a potential theory for the Wess--Zumino--Witten (WZW) equation in the space of Kähler potentials which is parallel to the potential theory for the Hermitian--Yang--Mills equation. A concept called $ω$-harmonicity on graphs is introduced which characterizes the WZW equation. We also show that, with respect to a Banach--Mazur type distance function, the distance between two solutions of the WZW equation is subharmonic. The harmonic map into the space of Kähler potentials, as a special case of the WZW equation, is also investigated. In particular, we show the solvability of the Dirichlet problem for the harmonic map, and the approximation/quantization by its finite dimensional counterparts. |
| title | A potential theory for the Wess--Zumino--Witten equation in the space of Kähler potentials |
| topic | Differential Geometry 32Q15, 32U05 |
| url | https://arxiv.org/abs/2410.00710 |