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A Wess–Zumino–Witten type equation in the space of Kähler potentials in terms of Hermitian–Yang–Mills metrics

Kuang-Ru Wu

Vol. 16 (2023), No. 2, 341–366
Abstract

We prove that the solution of a Wess–Zumino–Witten type equation from a domain D in m to the space of Kähler potentials can be approximated uniformly by Hermitian–Yang–Mills metrics on certain vector bundles. The key is a new version of Berndtsson’s theorem on the positivity of direct image bundles.

Keywords
Wess–Zumino–Witten, space of Kahler potentials, Hermitian–Yang–Mills
Mathematical Subject Classification 2010
Primary: 32Q15, 32U05, 53C55
Milestones
Received: 3 February 2020
Revised: 14 May 2021
Accepted: 5 July 2021
Published: 3 May 2023
Authors
Kuang-Ru Wu
Institute of Mathematics, Academia Sinica
Taipei
Taiwan

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