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

2015/04/23 by Costa, E., Ribeiro, E.
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1504.06212

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.

Related

• Estimates for Minimal Volume and Minimal Curvature on 4-dimensional compact manifolds
• Computations of the Yamabe invariant
• Volume of Riemannian manifolds, geometric inequalities, and homotopy theory
• Curvature, Covering Spaces, and Seiberg-Witten Theory
• Kodaira Dimension and the Yamabe Problem