A rigidity estimate for maps from S2$S^2$ to S2$S^2$ via the harmonic map flow

We show how a rigidity estimate introduced in recent work of Bernand‐Mantel, Muratov and Simon can be derived using the harmonic map flow. The estimate controls how far a degree one map between 2‐spheres can be from a Möbius map in terms of its energy, irrespective of whether or not the map has smal...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2023-02, Vol.55 (1), p.338-343
Main Author: Topping, Peter M.
Format: Article
Language:English
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Summary:We show how a rigidity estimate introduced in recent work of Bernand‐Mantel, Muratov and Simon can be derived using the harmonic map flow. The estimate controls how far a degree one map between 2‐spheres can be from a Möbius map in terms of its energy, irrespective of whether or not the map has small tension.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12731