https://neckpinch.com/authors/anton-alexa/New arXiv papers by Anton Alexa, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2512.08966/arxiv:2512.08966Mon, 01 Dec 2025 00:00:00 GMTAnton Alexa — We develop a dynamical method for proving the sharp Berezin-Li-Yau inequality. The approach is based on the volume-preserving mean curvature flow and a new monotonicity principle for the Riesz mean R_Λ(Ωₜ). For convex domains we show that R_Λ is monotone non-decreasing along the flow. The key input is a geometric correlation inequality between the boundary spectral density Q_Λ and the mean curvature H, established in all dimensions: in d=2 via a near-disk Fourier analysis, and in d≥ 3 via the boundary Weyl expansion together with a local spectral rigidity argument near the ball, with a first-zero exclusion principle closing the global step. Since the flow converges smoothly to the ball, the monotonicity implies the sharp Berezin-Li-Yau bound for every smooth convex domain. As an application, we obtain a sharp dynamical Cesàro-Pólya inequality for eigenvalue averages.Mean curvature flowVolume-preserving & constrained flowsHarnack inequalitiesStability & uniquenessLong-time existence & convergenceEigenvalues & spectrum