Small angle limits of Hamilton's footballs

Kewei Zhang; Yanir A. Rubinstein

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Small angle limits of Hamilton's footballs

Yanir A. Rubinstein, Kewei Zhang

Differential Geometry · Submitted 2 May 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we show that Hamilton's famous non-compact cigar soliton is the Gromov--Hausdorff limit of Hamilton's compact conical teardrop solitons.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,918 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.42 · compares with prior results 0.37 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Compact Ricci solitons on surfaces have at most two cone points, and are known as Hamilton's footballs.	background 1.00	0.05	0.04	asserted 1.00
s1	In this note we completely describe the degenerations of these footballs as one or both of the cone angles approaches zero.	contribution 0.99	0.92	0.36	asserted 1.00
s2	In particular, we show that Hamilton's famous non-compact cigar soliton is the Gromov--Hausdorff limit of Hamilton's compact conical teardrop solitons.	result 1.00	0.91	0.67	asserted 1.00

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The paper

Original 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.

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