Rayleigh–Faber–Krahn inequality

In spectral geometry, the Rayleigh–Faber–Krahn inequality, named after its conjecturer, Lord Rayleigh, and the 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 R n {\displaystyle \mathbb {R} ^{n}} , n ≥ 2 {\displaystyle n\geq 2} . It states that the first Dirichlet eigenvalue is no less than the corresponding Dirichlet eigenvalue of a Euclidean ball having the same volume.

Source: Wikipedia — Rayleigh–Faber–Krahn inequality (CC BY-SA 4.0)