On the structure of Ricci shrinkers

TL;DR

This paper develops a comprehensive structure theory for non-collapsed Ricci shrinkers without curvature restrictions, leading to new curvature estimates based solely on non-collapsing conditions.

Contribution

It introduces a novel structure theory for Ricci shrinkers that does not require curvature bounds, expanding understanding of their geometric properties.

Findings

Derived curvature estimates depending only on non-collapsing constants

Established foundational structure results for Ricci shrinkers without curvature assumptions

Enhanced the theoretical framework for analyzing Ricci shrinkers

Abstract

We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As applications, we obtain some curvature estimates of the Ricci shrinkers depending only on the non-collapsing constant.