As on arXiv
Abstract
We study the inverse curve shortening flow in the hyperbolic plane . We classify all solitons with respect to parabolic and conformal vector fields of . In the upper half-plane model of , we prove that parabolic solitons are all graphs on the -axis, whereas conformal solitons are graphs on the -axis. We study the concavity of these solitons and when they approach the coordinate axes.
Comments: 22 pages, 4 figures
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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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Geometric aspects of the curve shortening flow in the hyperbolic plane
Topics Curve shortening · Same authors Ivan Krznarić, Rafael López · Shared terms “hyperbolic plane”
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Non-uniqueness of curve shortening flow
Topics Curve shortening
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Monotonicity of the modulus under curve shortening flow
Topics Curve shortening
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Stabilization technique applied to curve shortening flow in
Topics Curve shortening
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Delayed parabolic regularity for curve shortening flow
Topics Curve shortening
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Curve shortening flow with an ambient force field
Topics Curve shortening
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On asymptotically conical curve shortening flows with convex projections
Topics Curve shortening
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A Compact Non-convex Ancient Curve Shortening Flow
Topics Curve shortening
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.