Effective volume growth of three-manifolds with positive scalar curvature

TL;DR

This paper establishes an effective linear volume growth rate for complete three-manifolds with non-negative Ricci curvature and positive scalar curvature, extending previous results using advanced geometric analysis techniques.

Contribution

It introduces a new approach based on $mbda$-bubbles and the almost-splitting theorem to prove volume growth estimates, building upon recent work by Chodosh-Li-Stryker.

Findings

Proves linear volume growth for specified three-manifolds.

Recovers and extends results by Munteanu-Wang.

Utilizes $mbda$-bubbles and Cheeger-Colding techniques.

Abstract

In this note, we prove an effective linear volume growth for complete three-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. This recovers the results obtained by Munteanu-Wang. Our method builds upon recent work by Chodosh-Li-Stryker, which utilizes the technique of $\mu$-bubbles and the almost-splitting theorem by Cheeger-Colding.