In spectral geometry, the Rayleigh–Faber–Krahn inequality, named after its conjecturer, Lord Rayleigh, and two individuals who independently proved the conjecture, G. Faber and Edgar Krahn, is an inequality concerning the lowest Dirichlet eigenvalue of the Laplace operator on a bounded domain in
Furthermore, the inequality is rigid in the sense that if the first Dirichlet eigenvalue is equal to that of the corresponding ball, then the domain must actually be a ball.
, the inequality essentially states that among all drums of equal area, the circular drum (uniquely) has the lowest voice.
[2] In particular, according to Cartan–Hadamard conjecture, it should hold in all simply connected manifolds of nonpositive curvature.
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