Stability, Finiteness and Dimension Four

Abstract

We prove that for any $k\in \mathbb{R},$ $v>0,$ and $D>0$ there are only finitely many diffeomorphism types of closed Riemannian $4$-manifolds with sectional curvature $\ge k,$ volume $\ge v,$ and diameter $\le D.$

arXiv comment40 figures

References in corpus (2)

• Semiconcave functions in Alexandrov's geometry
• Ricci flow and contractibility of spaces of metrics