Differential Geometry and Parametrization of 3D Knots

Tangent Point Self-Avoidance Energies for Curves

speaker: Heiko von der Mosel (Rheinisch-Westfälischen Technischen Hochschule Aachen)

abstract: I will report on joint work with Pavel Strzelecki. Let R_{tp} be the radius of the smallest circle that is tangent to a rectifiable curve \gamma at one point and passes through another curve point. Integrating over negative powers of this tangent-point interaction function yields a self-avoidance energy with topological and regularizing effects on \gamma. We discuss these effects in detail and show that this integral energy serves well as a knot energy bounding the number of isotopy types below a given energy value. Moreover we establish an explicit upper bound on the Hausdorff-distance of two space curves with finite energy that guarantees that these curves are ambient isotopic.

timetable:
Tue 28 Jun, 14:30 - 15:30, Aula Dini
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