Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning
Valentin Noël
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#MathematicalReasoning #SpectralGeometry #FormalLogic

Critical Lengths of Steklov Eigenvalues of Hypersurfaces of Revolution in Euclidean Space We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space and focus on the phenomenon of critical length, at which a Steklov eigenvalue is maximized. In this article, we conjecture that, in any dimension, there is a finite number of infinite critical length. To investigate this, we develop an algorithm to efficiently perform numerical experiments, providing support to our conjecture. Furthermore, we prove the conjecture in dimension n = 3 and n = 4.

"Critical Lengths of Steklov Eigenvalues of Hypersurfaces of Revolution in Euclidean Space" by Antoine Métras and Léonard Tschanz. #ExperimentalMath #SpectralGeometry #MathSky