A problem on a geometric property of lemniscates
Author: J. S. Hwang
Journal: Proc. Amer. Math. Soc. 82 (1981), 390-392
MSC: Primary 26C10; Secondary 30C15
MathSciNet review: 612726
Abstract: Let be the Eulcidean space and let be the product defined by , , , where is the distance between and . Let be the class of all such products with the same degree . For any product , we call the lemniscate of . We recently proved that if and are two products in such that , and if all zeros of lie on the same plane, then . We then asked whether this result is sharp. In this note, we answer this question in the affirmative sense.