Upper bounds for the second nonzero eigenvalue of the Laplacian via folding and conformal volume

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• Alexandre Girouard (Université Laval)
• Monday 23 March 2026, 14:00-15:00
• Seminar Room 1, Newton Institute.

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GSTW02 - Geometry of eigenvalues

We prove an upper bound for the volume-normalized second nonzero eigenvalue of the Laplace operator on closed Riemannian manifold, in terms of the conformal volume. This bound provides effective upper bound for a large class of manifolds, thereby generalizing many known results.   The proof uses the spherical cap folding mechanism originating in work of Nadirashvili in combination with the definition of the conformal volume of Li and Yau. This leads to very convenient admissible trial functions for the min-max characterisation of the second non-zero eigenvalue.   This is based on joint work with Mehdi Eddaoudi. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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