On Ricci curvature and volume growth in dimension three

TL;DR

This paper proves that three-dimensional manifolds with non-negative Ricci curvature and quadratic decay exhibit cubic volume growth, enhancing understanding of geometric properties under curvature constraints.

Contribution

It establishes a new volume growth result for 3D manifolds with specific Ricci curvature decay conditions, linking curvature decay to volume growth behavior.

Findings

Complete metrics on R^3 minus a ball with non-negative Ricci curvature have cubic volume growth.

Quadratic Ricci-curvature decay implies cubic volume growth in three dimensions.

The result connects curvature decay rates with global volume properties.

Abstract

We prove that any complete metric on R^3 minus a ball with non-negative Ricci curvature and quadratic Ricci-curvature decay, has cubic volume growth.