Minimal volume of complete uniform visibility manifolds with finite volume

TL;DR

This paper proves that complete uniform visibility manifolds with finite volume and sectional curvature between -1 and 0 have positive simplicial and minimal volumes, indicating they are geometrically complex.

Contribution

It establishes the positivity of simplicial and minimal volumes for a class of manifolds with specific curvature and visibility properties, linking geometric and topological invariants.

Findings

Complete uniform visibility manifolds of finite volume have positive simplicial volume.

Such manifolds also have non-zero minimal volume.

The results connect curvature bounds with topological complexity.

Abstract

We show that complete uniform visibility manifolds of finite volume with sectional curvature $-1 \leq K \leq 0$ have positive simplicial volumes. This implies that their minimal volumes are non-zero.