Bisection into small annuli

Moses Glasner, Richard Emanuel Katz and Mitsuru Nakai

Vol. 24 (1968), No. 3, 457–461

DOI: 10.2140/pjm.1968.24.457

Abstract

In a Riemannian manifold the modulus of a relatively compact set with border consisting of two sets of components is introduced to measure its magnitude from the viewpoint of harmonic functions. The existence of a subdivision into two sets each having modulus arbitrarily close to one is established.

Mathematical Subject Classification

Primary: 30.45

Milestones

Received: 17 March 1967

Published: 1 March 1968