As on arXiv
Abstract
Let be a Ricci shrinker such that and the measure induced by the weighted volume element is a probability measure. Given a point , we consider two probability measures defined in the tangent space , namely the Gaussian measure and the measure induced by the exponential map of to . In this paper, we prove a result that provides an upper estimate for the Wasserstein distance with respect to the Euclidean metric between the measures and , and which also elucidates the rigidity implications resulting from this estimate.
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Eigenvalue Estimates for Schrödinger Operators on Ricci Shrinkers
Topics Ricci solitons · Same authors Franciele Conrado, Detang Zhou · Shared terms “Ricci shrinkers”, “Let”
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Topics Ricci solitons · Same authors Franciele Conrado, Detang Zhou · Shared terms “Ricci shrinkers”
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Kähler–Ricci Shrinkers with Constant Scalar Curvature Are Rigid
Topics Stability & uniqueness, Ricci solitons · Same author Detang Zhou · Shared terms “Ricci shrinkers”, “Let”
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Topics Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”
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Rigidity of Kähler-Ricci Solitons with Constant Scalar Curvature
Topics Stability & uniqueness, Ricci solitons · Same author Detang Zhou · Shared terms “Let”
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Evolution of weights on a connected finite graph
Shared terms “probability measure”, “Wasserstein distance”
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Stability & uniqueness, Ricci solitons · Shared terms “Ricci shrinkers”
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.