A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary

2025/03/10 by Hong, Han, Wang, Gaoming · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.07009

Abstract

We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension n≥ 2 has λ₁(-αΔ+Ric)≥ 0 for some α<(4)/(n-1) and mean-convex boundary, then it is either isometric to Σ× ℝ_{≥ 0} for a closed manifold Σ with nonnegative Ricci curvature or it has no interior ends.

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