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M. Raffaelli:
"Nonrigidity of flat ribbons";
Vortrag: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes, Harvard University, Cambridge, MA, USA, online; 07.05.2021 - 09.05.2021.

Developable, i.e., flat, surfaces are classical objects in differential geometry, with lots of real-world applications within fields such as architecture or industrial design. In this talk I will discuss the problem of constructing a developable surface that contains a given space curve. The natural question here is the following. Given a curve, how many locally distinct developables can be defined along it? It turns out that, for any suitable choice of ruling angle (function measuring the angle between the ruling line and the curve's tangent vector) there exists a full circle of flat ribbons. In the second part of the talk we will examine the set of flat ribbons along a fixed curve in terms of energy. In particular, we will see that the classical rectifying developable of a curve maximizes the bending energy among all infinitely narrow flat ribbons having the same ruling angle. I will conclude by presenting some important open questions.