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Canonical Identification at Infinity for Ricci-Flat Manifolds

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Abstract

We give a natural way to identify between two scales, potentially arbitrarily far apart, in a non-compact Ricci-flat manifold with Euclidean volume growth when a tangent cone at infinity has smooth cross section. The identification map is given as the gradient flow of a solution to an elliptic equation.

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Acknowledgements

The author would like to thank Professor Tobias Holck Colding for numerous helpful discussions. The author was partially supported by NSF Grant DMS-1812142.

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  1. Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven, CT, 06511, USA

    Jiewon Park

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Park, J. Canonical Identification at Infinity for Ricci-Flat Manifolds. J Geom Anal 32, 8 (2022). https://doi.org/10.1007/s12220-021-00738-6

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