As on arXiv
Abstract
We formulate a uniqueness conjecture for curve shortening flow of proper curves on certain symmetric surfaces and give an example of a non-flat metric on the plane with respect to which curve shortening flow is not unique. That is, with respect to a suitably chosen metric, we construct a non-static solution to curve shortening flow starting from a properly embedded geodesic.
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.
-
The inverse curve shortening flow on the hyperbolic plane
Topics Curve shortening
-
Singularities of Curve Shortening Flow with Convex Projections
Topics Curve shortening, Stability & uniqueness
-
Monotonicity of the modulus under curve shortening flow
Topics Curve shortening
-
Delayed parabolic regularity for curve shortening flow
Topics Curve shortening · Shared terms “flow starting”
-
A Compact Non-convex Ancient Curve Shortening Flow
Topics Curve shortening
-
Compact curve shortening flow solutions out of non compact curve
Topics Curve shortening
-
Rotational Solitons for the Curve Shortening Flow on Revolution Surfaces
Topics Curve shortening
-
On asymptotically conical curve shortening flows with convex projections
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.