On the weakly conical expanding gradient Ricci solitons

2025/03/16 by Chan, Pak-Yeung, Lee, Man-Chun · 3 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.12416

Abstract

In this work, we construct several sequences of metrics on sphere with different limiting behaviors. By combining with the work of Deruelle, we use it and the localized maximum principle to construct various examples of expanding gradient Ricci solitons with positive curvature and exotic curvature decay. This answers a question proposed by Chow-Lu-Ni and also a question by Cao-Liu, respectively.

Cited by

• Curvature estimates for steady and expanding solitons in higher dimensions
• Higher-dimensional flying wing Steady Ricci Solitons
• Curvature pinching of asymptotically conical gradient expanding Ricci solitons

Related

• Asymptotic estimates and compactness of expanding gradient Ricci solitons
• Note on asymptotically conical expanding Ricci solitons
• Remarks on non-compact complete Ricci expanding solitons
• Smoothing out positively curved metric cones by Ricci expanders
• Expanding Ricci solitons with pinched Ricci curvature