4 papers
On the rate of convergence of the -curve shortening flow
Jean C. Cortissoz, Andrés Galindo, Alexander Murcia
In this paper we give rates of convergence for the -curve shortening flow for an integer, which improves on the known estimates and which are probably sharp.
The Ricci flow on a cylinder
Jean Cortissoz, Alexander Murcia
In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, result…
The Ricci flow on surfaces with boundary
Jean C. Cortissoz, Alexander Murcia
We show for a non homogeneous boundary value problem for the Ricci flow on the disk that when the initial metric has positive curvature and the boundary is convex then the initial…
On the stability of -fold circles and the dynamics of generalized curve shortening flows
Jean Cortissoz, Alexander Murcia
In this paper we study the (asymptotic and exponential) stability of the -fold circle as a solution of the -curve shortening flow ( an integer).