As on arXiv
Abstract
Let be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying for some . In this note, we give a new proof based on inverse mean curvature flow that is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow.
Comments: Final version to appear in J. Reine Angew. Math
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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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On the evolution of hypersurfaces along their inverse spacetime mean curvature
Topics Inverse mean curvature flow, Boundaries & non-compact, Other curvature flows · Same author Gerhard Huisken
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Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
Topics 3-manifolds · Shared terms “Ricci pinched”, “Lott”, “Hamilton”
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Manifolds with PIC1 pinched curvature
Topics 3-manifolds, Boundaries & non-compact · Shared terms “Topping”, “Deruelle”, “Schulze”
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Classification of ruled surfaces as homothetic self-similar solutions of the inverse mean curvature flow in the Lorentz-Minkowski 3-space
Topics Inverse mean curvature flow, 3-manifolds, Other curvature flows
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The -inverse mean curvature flow and the generalized Penrose conjecture
Topics Inverse mean curvature flow, Boundaries & non-compact, Other curvature flows · Shared terms “Let”
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Scalar curvature bounds for 3D continuous metrics through the Inverse Mean Curvature Flow
Topics Inverse mean curvature flow, 3-manifolds, Other curvature flows
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Three-manifolds with non-negatively pinched Ricci curvature
Topics 3-manifolds, Boundaries & non-compact · Shared terms “Deruelle”, “Schulze”, “Lott”
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Ruled surfaces as translating solitons of the inverse mean curvature flow in the three-dimensional Lorentz-Minkowski space
Topics Inverse mean curvature flow, 3-manifolds, Other curvature flows · Shared terms “Euclidean”
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
- 10A.1A Zoo of Three-Manifolds
The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.
- 10A.2Finite Rotation Groups and Spherical Space Forms
Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.
- 10A.4Homotopy Groups, Degree and the Hurewicz Theorem
Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.