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arXiv · 2610.28894

Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian

Mehdi Eddaoudi
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Abstract

We prove that Clarke critical metrics for the ratio of the first two eigenvalues of the conformal Laplacian on a closed manifold with positive Yamabe constant correspond to harmonic--Einstein maps into a sphere. We discuss some rigidity consequences, as well as an extension to the higher-order GJMS operators.

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Mehdi Eddaoudi. 2026-10-20. Harmonic-Einstein maps and critical metrics for eigenvalues of the conformal Laplacian. https://arxiv.org/abs/2610.28894

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