Convex curves of bounded type

Abstract

Let C be a simple closed convex curve in the plane for which the radius of curvature ρ is a continuous function of the arc length. Such a curve is called a convex curve of bounded type, if ρ lies between two fixed positive bounds. Here we give a new and simpler proof of Blaschke's Rolling Theorem. We prove one new theorem and suggest a number of open problems.

Keywords

• convex curve
• bounded type
• perimeter centroid
• Blaschke's rolling theorem
• parallel curve
• mass distribution on a curve.