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arXiv · 2601.16176

Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature

Alix Deleporte·Jean Lagacé·Marc Rouveyrol
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Abstract

Given a Riemannian manifold $M$ endowed with a smooth metric $g$ satisfying upper and lower sectional curvature bounds, we show an equivalence property between the $\mathrm{L}^2$ norm on $M$ and the $\mathrm{L}^2$ norm on subsets $\omega$ satisfying a thickness condition, for functions in the range of a spectral projector. The thickness condition is known to be optimal in this setting. The constant appearing in the equivalence of norms property depends only on the dimension of the manifold, curvature bounds, and frequency threshold of the spectral cutoff, but, crucially, not on the injectivity radius.

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Alix Deleporte, Jean Lagacé, Marc Rouveyrol. 2026-01-22. Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature. https://arxiv.org/abs/2601.16176

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