Selfsimilar expanders of the harmonic map flow

Details Selfsimilar expanders of the harmonic map flow Selfsimilar expanders of the harmonic map flow

2010-10-29

arxiv.org/abs/1010.6259v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

We study the existence, uniqueness, and stability of self-similar expanders
of the harmonic map heat flow in equivariant settings. We show that there exist
selfsimilar solutions to any admissiable initial data and that their uniqueness
and stability properties are essentially determined by the energy-minimising
properties of the so called equator maps.

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