If the L2 kernel of the Lichnerowicz Laplacian has dimension at most 3, then a complete 4D Ricci-flat ALE orbifold with Z2 at infinity is either the Eguchi-Hanson space or the flat orbifold R4/Z2.
On steady and expanding Ricci solitons with asymptotic symmetries
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abstract
We establish a symmetry principle for asymptotically cylindrical steady gradient Ricci solitons (GRSs) and asymptotically conical expanding GRSs with homogeneous links. Using this, we show that the Bryant steady soliton is the unique asymptotically cylindrical steady GRS that has a round spherical link and satisfies a particular quantitative rigidity condition. A similar characterization is proved for Bryant's expanding solitons. Finally, we establish a global symmetry result for GRSs which exhibit the aforementioned asymptotics with quotient-Berger sphere asymptotic links.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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An analytical characterization of Eguchi-Hanson space and its higher-dimensional analogs
If the L2 kernel of the Lichnerowicz Laplacian has dimension at most 3, then a complete 4D Ricci-flat ALE orbifold with Z2 at infinity is either the Eguchi-Hanson space or the flat orbifold R4/Z2.