EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 33(47), pp. 83--87 (1983)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home

EMIS Home

 		 

LEVEL SETS OF POLYNOMIALS IN SEVERAL REAL VARIABLES

C. H. Heiberg

U. S. Naval Academy, Annapolis, MD 21402, USA

Abstract: By generalizing the concept of homogeneous polynomial and by adapting Cauchy's technique for obtaining bounds on the zeros of polynomials in one complex variable, the level surfaces of a real polynomial in $E^n$ are studied with respect to their intersection with certain curves, including all lines, passing through the origin. In addition, it is shown that the equipotential surface of any axisymmetric harmonic polynomial in $E^3$ is unbounded if and only if it is asymptotic to a finite union of cones each of which is parallel to a cone having the origin as its vertex. \par This paper extends results obtained by M. Marden and P. A. McCoy in 1976.

Full text of the article:

Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition