Metric averaging in Euclidean and Hilbert spaces

Ralph Alexander

Vol. 85 (1979), No. 1, 1–9

DOI: 10.2140/pjm.1979.85.1

Abstract

A number of geometric properties of sets in l² can be measured in terms of maxima and minima of quadratic forms subject to side conditions. A method of metric addition which exploits this fact is investigated. The main objective is to develop a flexible method for attacking geometric extremal problems involving sums of distances or other metric constraints.

Mathematical Subject Classification 2000

Primary: 52A40

Milestones

Received: 5 March 1979

Published: 1 November 1979