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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniform bounds for isoperimetric problems
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by Jerrold Siegel and Frank Williams PDF
Proc. Amer. Math. Soc. 107 (1989), 459-464 Request permission

Abstract:

In this paper we generalize our previous joint work with Allan Calder on the width of homotopies by considering an arbitrary finite polyhedral pair $\left ( {W,V} \right )$ rather than $\left ( {I,\left \{ {0,1} \right \}} \right )$. We show that given appropriate topological conditions on a Riemannian manifold $M$, with respect to $\left ( {W.V} \right )$, there are bounds, ${B_q}\left ( {a,\left ( {W,V} \right ),M} \right )$, such that if $F:K \times W \to M$ is a map with ${\text {Lip}}\left ( {F\left | {\left ( {K \times V} \right )} \right .} \right ) < a$, then $F$ can be deformed ${\text {rel}}\left ( {K \times V} \right )$ to $F’$ with ${\text {Lip}}\left ( {F’} \right ) < {B_q}\left ( {a,\left ( {W,V} \right ),M} \right ) + \varepsilon$, where $\varepsilon > 0$ is arbitrary and $\dim \left ( K \right ) = q$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 459-464
  • MSC: Primary 55P99; Secondary 58E05
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0984815-2
  • MathSciNet review: 984815