Open Research Index

The fourth consecutive Dirichlet eigenvalue ratio

Jiachen Shi, Quanyu Tang

Palomar Registrypalomar/PALOMAR-2026-10-22-000012Oct 22, 2026math.SPscore 0

An unconditional Lean proof of the strict inequality lambda_5 / lambda_4 < C_N for every nonempty bounded connected open subset of Euclidean space of dimension at least two, with variational Dirichlet eigenvalues and the sharp Bessel-zero constant. No boundary regularity is assumed.

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