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Abstract
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We prove the existence of a center, or continuous selection of a point, in the relative interior
of
embedded
-disks in Riemannian
-manifolds.
If
the center can be made equivariant with respect to the isometries
of the manifold, and under mild assumptions the same holds for
. By contrast,
for every
there are examples where an equivariant center does not exist. The center can be
chosen to agree with any of the classical centers defined on the set of convex
compacta in the Euclidean space.
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Keywords
continuous selection, equivariant, proper actions, actions
on disks
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Mathematical Subject Classification 2010
Primary: 53C40, 54C65
Secondary: 52A20, 57S25
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Milestones
Received: 21 May 2018
Revised: 1 July 2019
Accepted: 12 July 2019
Published: 12 February 2020
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