Non-collapsing of Ricci shrinkers with bounded curvature

Key Points

• To explore uniform entropy bounds in Ricci shrinkers and extend non-collapsing results to smooth metric measure spaces.
• Establishes a uniform entropy bound for simply connected Ricci shrinkers.
• Analyzes the effects of a finite second homotopy group in this context.
• Extends results to a wider class of metric measure spaces under Bakry–Émery conditions.
• Demonstrates the presence of a uniform entropy bound in Ricci shrinkers with bounded curvature.
• Findings suggest the broader applicability of non-collapsing results to more general spaces.