Work

Global weak solutions of the Teichmüller harmonic map flow into general targets

Year: 2018

Type: article

Abstract: We analyse finite-time singularities of the Teichmüller harmonic map flow -- a natural gradient flow of the harmonic map energy -- and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover, we prove a no-loss-of-topology result at finite time, which completes the proof that this flow decomposes an arbitrary map into a collection of branched minimal immersions connected by curves.

Source: Analysis & PDE

DOI: 10.2140/apde.2019.12.815

Authors: Melanie Rupflin, Peter M. Topping

Institutions: University of Oxford, University of Warwick

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: Singularities of Geometric Partial Differential Equations, G8905719069