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arXiv · 2608.24532

Uniqueness for the K\"ahler-Yang-Mills equations

Vamsi Pritham Pingali·Chengjian Yao
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Abstract

A formula for the $\alpha$-K-energy functional for the K\"ahler-Yang-Mills (KYM) equations is provided in this paper. Using this formula and Chen's $\epsilon$-geodesic equation on the space of K\"ahler potentials, we prove that if a solution exists to the KYM equations for a simple vector bundle on a K\"ahler manifold with discrete automorphism group, then it is unique and the $\alpha$-K-energy is bounded from below. Inspired by the study of constant scalar curvature K\"ahler metrics, we introduce a coupled J-equation to study the $\alpha$-K energy functional.

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Vamsi Pritham Pingali, Chengjian Yao. 2026-08-25. Uniqueness for the K\"ahler-Yang-Mills equations. https://arxiv.org/abs/2608.24532

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