A relative entropy for expanders of the Harmonic map flow
Differential Geometry
2018-07-03 v1
Abstract
In this paper we focus on the uniqueness question for (expanding) solutions of the Harmonic map flow coming out of smooth 0-homogeneous maps with values into a closed Riemannian manifold. We introduce a relative entropy for two purposes. On the one hand, we prove the existence of two expanding solutions associated to any suitable solution coming out of a -homogeneous map by a blow-up and a blow-down process. On the other hand, generic uniqueness of expanding solutions coming out of the same 0-homogeneous map of 0 relative entropy is proved.
Cite
@article{arxiv.1807.00140,
title = {A relative entropy for expanders of the Harmonic map flow},
author = {Alix Deruelle},
journal= {arXiv preprint arXiv:1807.00140},
year = {2018}
}