MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Global curvature for rectifiable loops

Friedemann Schuricht and Heiko von der Mosel


We study in detail the notion of global curvature defined on rectifiable closed curves, a concept which has been successfully applied in existence and regularity investigation regarding elastic self-contact problems in nonlinear elasticity. A bound on this purely geometric quantity serves as an excluded volume constraint to prevent selfintersections of slender elastic bodies modeled as elastic rods. Moreover, a finite global curvature characterizes simple closed curves, whose arc length parameterizations possess a Lipschitz continuous tangent field. The investigation of local and non-local properties of global curvature motivates, in particular, an extended definition of local curvature at any point of a rectifiable loop. Finally we show how a bound on global curvature can be used to define topological constraints such as a given knot type for closed loops or a prescribed linking number for closed framed curves, suitable to describe, e.g., supercoiling phenomena of biomolecules.

MSC Codes:
53A04, 57M25, 74K10, 74M15, 92C40

Related publications

2003 Repository Open Access
Friedemann Schuricht and Heiko von der Mosel

Global curvature for rectifiable loops

In: Mathematische Zeitschrift, 243 (2003) 1, pp. 37-77