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Global weak solutions of the Teichmüller harmonic map flow into general targets
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Rupflin, Melanie and Topping, Peter (2019) Global weak solutions of the Teichmüller harmonic map flow into general targets. Analysis & PDE, 12 (3). pp. 815-842. doi:10.2140/apde.2019.12.815 ISSN 2157-5045.
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Official URL: https://doi.org/10.2140/apde.2019.12.815
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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Harmonic maps, Topology | ||||||||
| Journal or Publication Title: | Analysis & PDE | ||||||||
| Publisher: | Mathematical Sciences Publishers (MSP) | ||||||||
| ISSN: | 2157-5045 | ||||||||
| Official Date: | 2019 | ||||||||
| Dates: |
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| Volume: | 12 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 815-842 | ||||||||
| DOI: | 10.2140/apde.2019.12.815 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 4 July 2018 | ||||||||
| Date of first compliant Open Access: | 16 November 2018 | ||||||||
| RIOXX Funder/Project Grant: |
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