Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914273574256640 |
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| author | Deleporte, Alix Lagacé, Jean Rouveyrol, Marc |
| author_facet | Deleporte, Alix Lagacé, Jean Rouveyrol, Marc |
| contents | 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 $ω$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16176 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature Deleporte, Alix Lagacé, Jean Rouveyrol, Marc Analysis of PDEs Differential Geometry Optimization and Control Spectral Theory 35Q93, 58C40, 58J50, 93B05 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 $ω$ 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. |
| title | Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature |
| topic | Analysis of PDEs Differential Geometry Optimization and Control Spectral Theory 35Q93, 58C40, 58J50, 93B05 |
| url | https://arxiv.org/abs/2601.16176 |