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arXiv · 2608.17403

Green function asymptotics for the $\sigma_2$-Yamabe problem

Bin Deng·Han Lu
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Abstract

We establish, at every pole, the asymptotic expansion of the normalized $\Gamma_2$-Green function with a finite pole set in every dimension $n\ge5$. In dimensions $5\le n\le7$ the first correction is a unique nonnegative constant, whereas dimension $8$ exhibits a Weyl-driven $\sqrt{\log}$ term. For $n>8$ we construct the finite local curvature parametrix through the first positive indicial resonance and identify the first genuinely global coefficient by a relative Newton flux.

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Bin Deng, Han Lu. 2026-08-18. Green function asymptotics for the $\sigma_2$-Yamabe problem. https://arxiv.org/abs/2608.17403

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