As on arXiv
Abstract
In dimension , we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov-Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.
- Submitted
- Jan 8, 2017
- Last revised
- Feb 19, 2017 (v2)
- Subjects
- math.DG
Comments: 1 figure. Any comments are welcome
Its neighbourhood
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 2016, plus the canon.
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Rigidity of the round cylinders in Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”, “pointed Gromov”, “Hausdorff topology”
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Topics Limit spaces & RCD, Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”, “pointed Gromov”, “Gromov Hausdorff”
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Topics Limit spaces & RCD, Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics 4-manifolds, Limit spaces & RCD, Scalar curvature · Same author Yu Li · Shared terms “Ricci shrinkers”, “bounded scalar”, “Gromov Hausdorff”
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Heat kernel on Ricci shrinkers (II)
Topics Limit spaces & RCD, Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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On the rigidity of Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “pointed Gromov”, “Hausdorff topology”
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Topics Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “Gromov Hausdorff”
Read around it
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
- 6D.5Diffusions on Manifolds and Curvature
Brownian motion on a Riemannian manifold, the Bakry–Émery calculus, curvature-dimension inequalities, gradient estimates and log-Sobolev, coupling, and Brownian motion along a Ricci flow.
- 11B.2Ancient Solutions and the Harnack Inequality
Comparing curvature across space and time.
- 12A.6𝓛-Geodesics and the Variational Formulas
Perelman's §7.1 derived line by line: the first and second variation of 𝓛-length, 𝓛-Jacobi fields, adapted fields, Hamilton's Harnack expressions, and the differential inequalities for the reduced distance.