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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Majorization by hemispheres and quadratic isoperimetric constants
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by Paul Creutz PDF
Trans. Amer. Math. Soc. 373 (2020), 1577-1596 Request permission

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
  • 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.
  • © Copyright 2019 American Mathematical Society
  • 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
  • MathSciNet review: 4068274