Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4-manifolds

Abstract

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4-manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded.

To appear in Mathematische Nachrichten

References in corpus (3)

• Entropies, volumes, and Einstein metrics
• Monopole classes and Einstein metrics
• Estimates for Minimal Volume and Minimal Curvature on 4-dimensional compact manifolds