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Boundary Value Problems for the SU(∞)-Toda Equation via the Onofri Inequality
Abstract
We formulate and solve a degenerate elliptic boundary value problem for the SU(∞)-Toda equation on [0,1/2)×𝕊2. This constructs anti-self-dual Poincaré--Einstein metrics with circle symmetry on the $4$-ball and on complex line bundles over 𝕊2.
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BibTeX
@misc{chang2026boundary,
title = {{Boundary Value Problems for the $SU(\infty)$-Toda Equation via the Onofri Inequality}},
author = {Sun-Yung Alice Chang and Hongyi Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37282},
eprint = {2609.37282},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37282},
}
RIS
TY - UNPB
TI - Boundary Value Problems for the SU(∞)-Toda Equation via the Onofri Inequality
AU - Sun-Yung Alice Chang
AU - Hongyi Liu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37282
UR - https://arxiv.org/abs/2609.37282
AB - We formulate and solve a degenerate elliptic boundary value problem for the SU(∞)-Toda equation on [0,1/2)×𝕊^2. This constructs anti-self-dual Poincaré--Einstein metrics with circle symmetry on the $4$-ball and on complex line bundles over 𝕊^2.
ER -