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arXiv · 2609.37282

Boundary Value Problems for the $SU(\infty)$-Toda Equation via the Onofri Inequality

Sun-Yung Alice Chang·Hongyi Liu
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Abstract

We formulate and solve a degenerate elliptic boundary value problem for the $SU(\infty)$-Toda equation on $[0,\frac12)\times\mathbb{S}^2$. This constructs anti-self-dual Poincaré--Einstein metrics with circle symmetry on the $4$-ball and on complex line bundles over $\mathbb{S}^2$.

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Sun-Yung Alice Chang, Hongyi Liu. 2026-09-29. Boundary Value Problems for the $SU(\infty)$-Toda Equation via the Onofri Inequality. https://arxiv.org/abs/2609.37282

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