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Continuous pursuit curves on cat \((K)\) spaces

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Abstract

We prove theorems of existence, uniqueness and rate of convergence for continuous pursuit curves in cat \((K)\) spaces. We prove that these pursuit curves have a regularity property that serves as a replacement for \(C^{1,1}\) regularity in smooth spaces.

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Acknowledgments

The author would like to express his gratitude to Professor S. Alexander and Professor R. Bishop for their suggestions and advice. He is grateful to Professor R. Ghrist for his support during the preparation of this article. He thanks Professor D. Berg for his suggestion to get a short proof of Lemma 4. Also he thanks the referee and Professor A. Lytchak for their valuable comments. The material in this paper is part of the author’s thesis [13]. He gratefully acknowledge support from the ONR Antidote MURI project, Grant No. N00014-09-1-1031.

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  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Chanyoung Jun

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  1. Chanyoung Jun
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Correspondence to Chanyoung Jun.

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Jun, C. Continuous pursuit curves on cat \((K)\) spaces. Geom Dedicata 173, 309–330 (2014). https://doi.org/10.1007/s10711-013-9944-0

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  • DOI: https://doi.org/10.1007/s10711-013-9944-0

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