Stability, Finiteness and Dimension Four

2020/06/03 by Curtis Pro, Pro, Curtis, Frederick Wilhelm +1
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.2006.02450

40 figures

arxiv created 2020/06/03 · arxiv updated 2020/06/05

Abstract

We prove that for any k∈ ℝ, v>0, and D>0 there are only finitely many diffeomorphism types of closed Riemannian 4-manifolds with sectional curvature ≥ k, volume ≥ v, and diameter ≤ D.

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