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Riemannian and Kahler flying wing steady Ricci solitons

Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis August 21, 2024 - August 23, 2024

August 21, 2024 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Yi Lai (Stanford University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Riemannian and Kahler flying wing steady Ricci solitons

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Steady Ricci solitons are fundamental objects in the study of Ricci flow, as they are self-similar solutions and often arise as singularity models. Classical examples of steady solitons are the most symmetric ones, such as the 2D cigar soliton, the O(n)-invariant Bryantsolitons, and Cao’s U(n)-invariant Kahler steady solitons. Recently we constructed a family of flying wing steady solitons in any real dimension n≥3, which confirmed a conjecture by Hamilton in n=3. In dimension 3, we showed all steady gradient solitons are O(2)-symmetric. In the Kahler case, we also construct a family of Kahler flying wing steady gradient solitons with positive curvature for any complex dimension n≥2. This answers a conjecture by H.-D.Cao in the negative. This is partly collaborated with Pak-Yeung Chan and Ronan Conlon.

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Riemannian and Kahler flying wing steady Ricci solitons

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