As on arXiv
Abstract
Given two disjoint nested embedded closed curves in the plane, both evolving under curve shortening flow, we show that the modulus of the enclosed annulus is monotonically increasing in time. An analogous result holds within any ambient surface satisfying a lower curvature bound.
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 2021, plus the canon.
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Delayed parabolic regularity for curve shortening flow
Topics Curve shortening · Same authors Arjun Sobnack, Peter M. Topping
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The Harnack inequality without convexity for curve shortening flow
Topics Curve shortening · Same authors Arjun Sobnack, Peter M. Topping
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A delayed interior area-to-height estimate for the Curve Shortening Flow
Topics Curve shortening · Same author Arjun Sobnack
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Non-uniqueness of curve shortening flow
Topics Curve shortening
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Curve shortening flow with an ambient force field
Topics Curve shortening · Shared terms “curvature bounds”
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The inverse curve shortening flow on the hyperbolic plane
Topics Curve shortening
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Stabilization technique applied to curve shortening flow in
Topics Curve shortening
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Curve shortening flows on surfaces that are not convex at infinity
Topics Curve shortening · Shared terms “embedded closed”, “closed curves”, “increasing”
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
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.
- 12C.4Loops, Disks and Curve Shrinking
Perelman III §§2–3 and Morgan–Tian §§18.3–18.7: π₃ as spheres of loops, minimal disks and the −2π estimate, curve shrinking, ramps in M × S¹ and the estimates that make the argument rigorous.