Small angle limits of Hamilton's footballs

Abstract

Compact Ricci solitons on surfaces have at most two cone points, and are known as Hamilton's footballs. In this note we completely describe the degenerations of these footballs as one or both of the cone angles approaches zero. In particular, we show that Hamilton's famous non-compact cigar soliton is the Gromov--Hausdorff limit of Hamilton's compact conical teardrop solitons.