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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Majorization by hemispheres and quadratic isoperimetric constants


Author: Paul Creutz
Journal: Trans. Amer. Math. Soc. 373 (2020), 1577-1596
MSC (2010): Primary 46B09, 53A10; Secondary 52A38, 53C60, 46B20
DOI: https://doi.org/10.1090/tran/7827
Published electronically: November 12, 2019
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Abstract: Let $ X$ be a Banach space or more generally a complete metric space admitting a conical geodesic bicombing. We prove that every closed $ L$-Lipschitz curve $ \gamma :S^1\rightarrow X$ may be extended to an $ L$-Lipschitz map defined on the hemisphere $ f:H^2\rightarrow X$. This implies that $ X$ satisfies a quadratic isoperimetric inequality (for curves) with constant $ \frac {1}{2\pi }$. We discuss how this fact controls the regularity of minimal discs in Finsler manifolds when applied to the work of Alexander Lytchak and Stefan Wenger.


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Additional Information

Paul Creutz
Affiliation: Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
Email: pcreutz@math.uni-koeln.de

DOI: https://doi.org/10.1090/tran/7827
Received by editor(s): October 30, 2018
Received by editor(s) in revised form: February 6, 2019, and February 12, 2019
Published electronically: November 12, 2019
Additional Notes: The author was partially supported by the DFG grant SPP 2026.
Article copyright: © Copyright 2019 American Mathematical Society