Extremal metrics for Laplace eigenvalues in perturbed conformal classes on 
products

Matthiesen, Henrik

doi:10.1007/s12220-018-0082-7

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Extremal metrics for Laplace eigenvalues in perturbed conformal classes on products

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Matthiesen, Henrik
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s12220-018-0082-7
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Citation

Matthiesen, H. (2019). Extremal metrics for Laplace eigenvalues in perturbed conformal classes on products. Journal of Geometric Analysis, 29(3), 2456-2468. doi:10.1007/s12220-018-0082-7.

Cite as: https://hdl.handle.net/21.11116/0000-0004-4055-4

Abstract

In this short note, we prove that conformal classes which are small perturbations of a
product conformal class on a product with a standard sphere admit a metric extremal
for some Laplace eigenvalue. As part of the arguments, we obtain perturbed harmonic
maps with constant density.