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

TL;DR

This paper investigates relationships between minimal volume invariants, topological properties, and curvature conditions on 4-manifolds, establishing new estimates and sphere theorems under curvature bounds.

Contribution

It introduces new estimates involving Yamabe minimal volume and topological invariants, and proves topological sphere theorems for submanifolds with bounded second fundamental form.

Findings

Establishes bounds relating minimal volume invariants and topology.

Proves sphere theorems for submanifolds with curvature constraints.

Provides new curvature estimates 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.