Vol. 66, No. 2, 1976

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Level sets of polynomials in n real variables

Morris Marden and Peter A. McCoy

Vol. 66 (1976), No. 2, 491–498

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
Received: 3 October 1974
Published: 1 October 1976
Morris Marden
Peter A. McCoy