, Volume 18, Issue 3, pp 505–517 | Cite as

Lipschitz and Hölder continuity results for some functions of cones

  • Alberto SeegerEmail author


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.


Convex cone Maximal angle Incenter Circumcenter Solidity coefficient Sharpness coefficient  Lipschitz continuity Hölder continuity 

Mathematics Subject Classification (2000)

26A12 26B35 56A55 52A40 90C25 90C26 



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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© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AvignonAvignonFrance

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