Flujo general de la reducción de la curvatura

Abstract

The curve shortening flow is a process that modifies a curve in the normal direction with a speed equal to the curvature at each point and from there has been used to analyze the behavior of curves that are encoded with time involving aspects such as tangent and normal vector, so it is of great interest within differential geometry. That is why we are going to study the curve shortening flow starting with some previous concepts, an explanation of the phenomenon and later we will obtain a result that will determine the heat equation that does not allow us to study our problem, so we are going to describe the curve shortening flow using the Frenet tryro. Then we will study this phenomenon in flat curves and its equivalence with a partial differential equation.