Ends of (singular) Ricci shrinkers

TL;DR

This paper investigates the structure and number of ends of Ricci shrinkers, including singular ones, and explores implications for limits of sequences of Ricci shrinkers, especially regarding the formation of conical ends.

Contribution

It provides estimates on the number of ends of Ricci shrinkers and analyzes the behavior of their limits, particularly ruling out new conical ends in the limit.

Findings

Bound on the number of ends of Ricci shrinkers.

No new conical ends can form in limits of Ricci shrinker sequences.

Applications to the convergence behavior of Ricci shrinkers.

Abstract

We estimate the number of ends of smooth and singular Ricci shrinkers focussing first on general ends and later on asymptotically conical ones. In particular, we obtain a variety of applications to sequences of Ricci shrinkers converging in a weak pointed sense to a possibly singular limit Ricci shrinker, for instance no new conical end can form in the limit.