Centers of disks in Riemannian manifolds

We prove the existence of a center, or continuous selection of a point, in the relative interior of $C^{1}$ embedded $k$ -disks in Riemannian $n$ -manifolds. If $k \leq 3$ the center can be made equivariant with respect to the isometries of the manifold, and under mild assumptions the same holds for $k = 4 = n$ . By contrast, for every $n \geq k \geq 6$ 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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/pjm

We have not been able to recognize your IP address 18.210.12.229 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

continuous selection, equivariant, proper actions, actions on disks

Mathematical Subject Classification 2010

Primary: 53C40, 54C65

Secondary: 52A20, 57S25

Milestones

Received: 21 May 2018

Revised: 1 July 2019

Accepted: 12 July 2019

Published: 12 February 2020

Authors

Igor Belegradek
School of Mathematics Georgia Institute of Technology Atlanta, GA United States

Mohammad Ghomi
School of Mathematics Georgia Institute of Technology Atlanta, GA United States

Vol. 304, No. 2, 2020

Igor Belegradek and Mohammad Ghomi

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors