arXiv subjects

Márcio Rostirolla Adames

Publications and source records attributed to Márcio Rostirolla Adames.

2 recordsLinked to original sources

arXiv2015

A note on self-similar solutions of the curve shortening flow

This article gives an alternative approach to the self-shrinking and self-expanding solutions of the curve shortening flow, which are related to singularity formation of the mean curvature flow. The motivation for the self-similar solutions arises from natural area preserving rescaling. Further we describe the self-similar solutions in terms of a simple ODE and give an alternative proof that they lie in planes.

math.DG↗

arXiv2013

Spacelike Self-Similar Shrinking Solutions of the Mean Curvature Flow in Pseudo-Euclidean Spaces

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cases. The classification is analogous to the existing classifications in the euclidean case of Huisken and Smoczyk.

math.DG↗