Convex functions with restricted curvature

Styer, D.; Wright, D. J.

doi:10.1090/S0002-9939-1990-1010002-6

Convex functions with restricted curvature
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by D. Styer and D. J. Wright PDF

Proc. Amer. Math. Soc. 109 (1990), 981-990 Request permission

Abstract:

Given $0 \leq {R_1} \leq {R_2} \leq \infty$, we consider a class of normalized convex functions $f$ in the unit disk ${\mathbf {D}}$, for which $\partial f({\mathbf {D}})$ satisfies a Blaschke Rolling Theorem condition with radii ${R_1}$ and ${R_2}$. This class contains the convex functions of bounded type. We study the geometry of the image region $f({\mathbf {D}})$ and various covering and distortion properties.

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A comprehensive introduction to differential geometry

Note on the curvature of level curves of Green’s function

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