Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

Author: 

Kohout, J
Rupflin, M
Topping, P

Publication Date: 

24 March 2020

Journal: 

Advances in Calculus of Variations

Last Updated: 

2021-04-09T18:19:37.78+01:00

DOI: 

10.1515/acv-2019-0086

abstract: 

The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as t→∞.

Symplectic id: 

1087021

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article