A sharp spectral splitting theorem

2024/12/17 by Gioacchino Antonelli, Antonelli, Gioacchino, Marco Pozzetta +3 · 1 citation
Mathematics · #advanced mathematical theories #Spectral Theory in Mathematical Physics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2412.12707

Abstract

We prove a sharp spectral generalization of the Cheeger--Gromoll splitting theorem. We show that if a complete non-compact Riemannian manifold M of dimension n≥ 2 has at least two ends and λ₁(-γΔ+Ric)≥ 0, for some γ<(4)/(n-1), then M splits isometrically as \mathbb R× N for some compact manifold N with nonnegative Ricci curvature. We show that the constant (4)/(n-1) is sharp, and the multiple-end assumption is necessary for any γ>0.

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• Connected sum of manifolds with spectral Ricci lower bounds

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