On the total curvature of minimizing geodesics on convex surfaces

TL;DR

This paper establishes a universal upper bound for the total curvature of minimizing geodesics on convex surfaces in Euclidean space, providing a fundamental geometric constraint.

Contribution

It introduces a universal upper bound for the total curvature of minimizing geodesics on convex surfaces, advancing understanding of their geometric properties.

Findings

Universal upper bound for total curvature established

Applicable to all convex surfaces in Euclidean space

Enhances geometric analysis of convex surfaces

Abstract

We give a universal upper bound for the total curvature of minimizing geodesic on a convex surface in the Euclidean space.