On the behavior of the omitted arc of a support point of the class

Abstract

In this article, we consider the hypothetical nonmonotonicity of the arguments of the vectors tracing the omitted arc of a support point of the class and tangent to it. We show that the number of sign changes of (arg w(t))′ and (arg w′(t))′ on the omitted arc are finite.

†Dedicated to Professor Peter L. Duren, who made significant contributions to the theory of support points, on the occasion of his 70 th birthday.

Keywords:

• Support point
• Omitted arc
• Wiggle point
• Waver point

Keywords:

• 2000 Mathematics Subject Classification
• Primary: 30C45

Notes

†Dedicated to Professor Peter L. Duren, who made significant contributions to the theory of support points, on the occasion of his 70 th birthday.