Weak Ricci curvature bounds for Ricci shrinkers

TL;DR

This paper demonstrates that in complete Ricci shrinkers, there exists a sequence of points at infinity where the Ricci tensor's norm grows at most linearly, revealing new geometric behavior of these manifolds.

Contribution

It establishes a linear growth bound for the Ricci tensor along a sequence tending to infinity in complete Ricci shrinkers, a novel geometric insight.

Findings

Existence of a sequence with controlled Ricci growth at infinity

Linear growth bound for Ricci tensor norms in Ricci shrinkers

Advances understanding of Ricci shrinker geometry

Abstract

We show that for a complete Ricci shrinker there exists a sequence of points tending to infinity whose norms of the Ricci tensor grow at most linearly.