Riemannian geometry

Cheeger constant

In Riemannian geometry, the Cheeger isoperimetric constant of a compact Riemannian manifold M is a positive real number h(M) defined in terms of the minimal area of a hypersurface that divides M into two disjoint pieces. In 1970, Jeff Cheeger proved an inequality that related the first nontrivial eigenvalue of the Laplace–Beltrami operator on M to h(M). This proved to be a very influential idea in Riemannian geometry and global analysis and inspired an analogous theory for graphs. (Wikipedia).

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Related pages

Compact space | Graph (discrete mathematics) | Global analysis | Ricci curvature | Spectral gap | Cheeger constant (graph theory) | Surface area | Laplace–Beltrami operator | Riemannian manifold | Hypersurface | Salomon Bochner | Riemannian geometry | Closed manifold