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<p>In this paper, we will establish elliptic regularity estimates on families of gravitational instantons whose model metric near infinity collapse to a flat 3 dimensional space. We show that the constants in these estimates can be chosen uniformly for the whole family of metrics. We apply these results to the Laplacian and show it is Fredholm. We also determine between which weighted spaces it is an isomorphism.</p>

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Elliptic Analysis on Collapsing Gravitational Instantons Modelled Using the Gibbons-Hawking Ansatz

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Willem Adriaan Salm

摘要

In this paper, we will establish elliptic regularity estimates on families of gravitational instantons whose model metric near infinity collapse to a flat 3 dimensional space. We show that the constants in these estimates can be chosen uniformly for the whole family of metrics. We apply these results to the Laplacian and show it is Fredholm. We also determine between which weighted spaces it is an isomorphism.