Level sets of polynomials in n real variables

Morris Marden and Peter A. McCoy

Vol. 66 (1976), No. 2, 491–498

DOI: 10.2140/pjm.1976.66.491

Abstract

The methods used in studying the zeros of a polynomial in a single complex variable are here adapted to investigating the level surfaces of a real polynomial in Eⁿ, with respect to their intersection and finite or asymptotic tangency with certain cones. Special attention is given to the equipotential surfaces generated by an axisymmetric harmonic polynomial in E³.

Mathematical Subject Classification

Primary: 26A78, 26A78

Secondary: 30A08

Milestones

Received: 3 October 1974

Published: 1 October 1976