Add to ORKGIn this paper, we study the curve shortening flow (CSF) on Riemann surfaces. We generalize Huisken's comparison function to Riemann surfaces and surfaces with conic singularities. We reprove the Gage-Hamilton-Grayson theorem on surfaces. We also prove that for embedded simple closed curves, CSF can not touch conic singularities with cone angles $\leq \pi$.Comment: 31 pages, 4 figures. Accepted versio
In this paper, curve shortening flow in Euclidian space R-n(n >= 3) is studied, and S. Altschuler...
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric ...
AbstractThe blow-up rates of derivatives of the curvature function will be presented when the closed...
We consider embedded, smooth curves in the plane which are either closed or asymptotic to two lines....
In this thesis we consider closed, embedded, smooth curves in the plane whose local total curvature ...
The three geodesics theorem of Lusternik and Schnirelmann asserts that for every Riemannian metric o...
We prove a comparison theorem for the isoperimetric profiles of simple closed curves evolving by the...
The three geodesics theorem of Lusternik and Schnirelmann asserts that for every Riemannian metric o...
The three geodesics theorem of Lusternik and Schnirelmann asserts that for every Riemannian metric o...
Abstract. We prove a comparison theorem for the isoperimetric pro-files of simple closed curves evol...
PhD ThesesThis work considers problems pertaining to the regularity theory and the analysis of sing...
We study ¿flat knot types¿ of geodesics on compact surfaces M2. For every flat knot type and any Rie...
Abstract. We prove that the only closed, embedded ancient solutions to the curve shortening flow on ...
A new isoperimetric estimate is proved for embedded closed curves evolving by curve shortening flow,...
Based on the recent work by Andrews and Bryan [2] we present a new proof of the celebrated Grayson's...
In this paper, curve shortening flow in Euclidian space R-n(n >= 3) is studied, and S. Altschuler...
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric ...
AbstractThe blow-up rates of derivatives of the curvature function will be presented when the closed...
We consider embedded, smooth curves in the plane which are either closed or asymptotic to two lines....
In this thesis we consider closed, embedded, smooth curves in the plane whose local total curvature ...
The three geodesics theorem of Lusternik and Schnirelmann asserts that for every Riemannian metric o...
We prove a comparison theorem for the isoperimetric profiles of simple closed curves evolving by the...
The three geodesics theorem of Lusternik and Schnirelmann asserts that for every Riemannian metric o...
The three geodesics theorem of Lusternik and Schnirelmann asserts that for every Riemannian metric o...
Abstract. We prove a comparison theorem for the isoperimetric pro-files of simple closed curves evol...
PhD ThesesThis work considers problems pertaining to the regularity theory and the analysis of sing...
We study ¿flat knot types¿ of geodesics on compact surfaces M2. For every flat knot type and any Rie...
Abstract. We prove that the only closed, embedded ancient solutions to the curve shortening flow on ...
A new isoperimetric estimate is proved for embedded closed curves evolving by curve shortening flow,...
Based on the recent work by Andrews and Bryan [2] we present a new proof of the celebrated Grayson's...
In this paper, curve shortening flow in Euclidian space R-n(n >= 3) is studied, and S. Altschuler...
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric ...
AbstractThe blow-up rates of derivatives of the curvature function will be presented when the closed...