A potential theory for the Wess--Zumino--Witten equation in the space of Kähler potentials

2024/10/01 by Wu, Kuang-Ru · 2 citations
#32Q15 #32U05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.00710

Abstract

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.

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• Uniform RC-positivity of direct image bundles
• Canonical metrics on families of vector bundles

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