Optimal rates for curvature flows on the circle (2016)
"In this thesis we will study the stability of the convergence for the solutions to the normalized p-curve shorteningflow (p-CSF). In the first chapter we Will explain what the p-curve shortening flow is, and the most important results regarding the convergence and stability of its solutions. In chapter two, we Will explain what is the problem with the eigenvalues of the linearization of the p-curve shortening flow, and how this prevent us to use the standard methods to show stability for the p-CSF. In the third and final chapter, we Will present our main result which is that the normalized solution to the p-CSF converges at a rate of e-(3P-l) towards 1; what is really interesting is that 3p ? 1 is the second eigenvalue of the linearimtion of the original problem". -- Tomado del resumen.