On an area-preserving inverse curvature flow of convex closed plane curves

2021 ◽  
Vol 280 (8) ◽  
pp. 108931
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Area Preserving ◽  
Closed Plane

On a length-preserving inverse curvature flow of convex closed plane curves

2020 ◽  
Vol 269 (7) ◽  
pp. 5802-5831
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Closed Plane

An anisotropic area-preserving flow for convex plane curves

2019 ◽  
Vol 266 (6) ◽  
pp. 3764-3786
Author(s):  
Shengliang Pan ◽  
Yunlong Yang
Keyword(s):  
Plane Curves ◽  
Convex Plane ◽  
Area Preserving

2. Applications of the Theorem that Two Closed Plane Curves intersect an even number of times

1878 ◽  
Vol 9 ◽  
pp. 237-246 ◽  
Author(s):  
Tait
Keyword(s):  
Special Class ◽  
Double Point ◽  
Closed Curve ◽  
British Association ◽  
Plane Curves ◽  
Double Points ◽  
The Wire ◽  
Closed Plane

The theorem itself may be considered obvious, and is easily applied, as I showed at the late meeting of the British Association, to prove that in passing from any one double point of a plane closed curve continuously along the curve to the same point again, an even number of intersections must be passed through. Hence, if we suppose the curve to be constructed of cord or wire, and restrict the crossings to double points, we may arrange them throughout so that, in following the wire continuously, it goes alternately over and under each branch it meets. When this is done it is obviously as completely knotted as its scheme (defined below) will admit of, and except in a special class of cases cannot have the number of crossings reduced by any possible deformation.

Parity conditions for realizability of Gauss diagrams

2019 ◽  
Vol 28 (01) ◽  
pp. 1950015
Author(s):  
Oleg N. Biryukov
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Plane Curves ◽  
Double Points ◽  
Gauss Diagram ◽  
Necessary And Sufficient ◽  
Closed Plane

We consider a problem of realizability of Gauss diagrams by closed plane curves where the plane curves have only double points of transversal self-intersection. We formulate the necessary and sufficient conditions for realizability. These conditions are based only on the parity of double and triple intersections of the chords in the Gauss diagram.

scholarly journals Contracting convex immersed closed plane curves with slow speed of curvature

2012 ◽  
Vol 364 (11) ◽  
pp. 5735-5763 ◽  
Author(s):  
Yu-Chu Lin ◽  
Chi-Cheung Poon ◽  
Dong-Ho Tsai
Keyword(s):  
Plane Curves ◽  
Slow Speed ◽  
Closed Plane
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