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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00710 |
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Table of 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.