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Lipschitz and Hölder continuity results for some functions of cones

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Abstract

We prove the Lipschitz continuity of the maximal angle function on the set of closed convex cones in a Hilbert space. A similar result is obtained for the minimal angle function. On the other hand, we prove that the incenter of a solid cone and the circumcenter of a sharp cone behave in a locally Hölderian manner.

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Acknowledgments

The author would like to thank the referee for meticulous reading of the manuscript and for several suggestions that improved the presentation.

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  1. Department of Mathematics, University of Avignon, 33 rue Louis Pasteur, 84000 , Avignon, France

    Alberto Seeger

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  1. Alberto Seeger
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Correspondence to Alberto Seeger.

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Seeger, A. Lipschitz and Hölder continuity results for some functions of cones. Positivity 18, 505–517 (2014). https://doi.org/10.1007/s11117-013-0258-0

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  • DOI: https://doi.org/10.1007/s11117-013-0258-0

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