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arXiv · 2203.01711

Optimal coordinates for Ricci-flat conifolds

Klaus Kroencke·Áron Szabó
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Abstract

We compute the indicial roots of the Lichnerowicz Laplacian on Ricci-flat cones and give a detailed description of the corresponding radially homogeneous tensor fields in its kernel. For a Ricci-flat conifold $(M,g)$ which may have asymptotically conical as well as conically singular ends, we compute at each end a lower bound for the order with which the metric converges to the tangent cone. As a special subcase of our result, we show that any Ricci-flat ALE manifold $(M^n,g)$ is of order $n$ and thereby close a small gap in a paper by Cheeger and Tian.

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Klaus Kroencke, Áron Szabó. 2022-03-03. Optimal coordinates for Ricci-flat conifolds. https://arxiv.org/abs/2203.01711

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