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- W4213406334 abstract "The resolution of the $G_2$-orbifold $T^7/Gamma$, where $Gamma$ is a suitably chosen finite group, admits a $1$-parameter family of $G_2$-structures with small torsion $varphi^t$, obtained by gluing in Eguchi-Hanson spaces. It was shown by Joyce that $varphi^t$ can be perturbed to torsion-free $G_2$-structures $tilde{varphi}^t$ for small values of $t$. Using norms adapted to the geometry of the manifold we give an alternative proof of the existence of $tilde{varphi}^t$. This alternative proof produces the estimate $left|left| tilde{varphi}^t-varphi^t right|right|_{C^0} leq ct^{5/2}$. This is an improvement over the previously known estimate $left|left| tilde{varphi}^t-varphi^t right|right|_{C^0} leq ct^{1/2}$. As part of the proof, we show that Eguchi-Hanson space admits a unique (up to scaling) harmonic form with decay, which is a result of independent interest." @default.
- W4213406334 created "2022-02-24" @default.
- W4213406334 creator A5085036471 @default.
- W4213406334 date "2020-11-01" @default.
- W4213406334 modified "2023-09-23" @default.
- W4213406334 title "Improved Estimates for $G_2$-structures on the Generalised Kummer Construction" @default.
- W4213406334 hasPublicationYear "2020" @default.
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