Doubling inequalities for eigenfunctions

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• Eugenia Malinnikova (Stanford University)
• Thursday 05 February 2026, 09:30-10:30
• Seminar Room 1, Newton Institute.

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

Doubling inequalities quantify local growth properties of eigenfunctions, bound their vanishing order, and provide a basic quantitative form of unique continuation. They have become a standard tool in spectral geometry and related PDE questions, including bounds for nodal and singular sets. I will give an overview of doubling estimates for Laplace eigenfunctions on manifolds, as well as various methods, used in the proof of such inequalities: Carleman estimates in the tradition of Donnelly–Fefferman, geometric arguments via harmonic extension/lift, and a new propagation-of-smallness approach. If time permits, I will briefly discuss boundary analogues and current work on doubling in the presence of conic singularities.

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

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