The inner mapping radius of harmonic mappings of the unit disk

Abstract

The class S_n consists of univalent, harmonic, and sense-preserving functions J unit disk δ such that where . Using a technique from Clinic and Shell-Small, we construct a family of I-slit mappings in S_p by varying . As W(z) changes, the tin of the slit slides along the negative real axis from the point U to - 1 In doing so. we establish that the inner mapping radius p(f) can be as large as 4. In addition, we show that the inner mapping radius for functions in can be as small as 1/2 and as large as 2.

AMS No.:

• Koebe theorem
• mapping radius
• harmonic mappings
• 30C20

^*Dedicated to A. W. Goodman on the occasion of his eightieth birthday.

^*Dedicated to A. W. Goodman on the occasion of his eightieth birthday.

Notes

^*Dedicated to A. W. Goodman on the occasion of his eightieth birthday.