 |
Universität Augsburg
|
|
|
Universität Augsburg
|
|
Frau Anna Lagemann
Universität Aachen
spricht am
Montag, 28. November 2022
um
16 Uhr s.t.
im
2004/L1 und Zoom (hybride Veranstaltung)
über das Thema:
| Abstract: |
|
Planar closed immersed curves can be classified by the Whitney-Graustein theorem in terms of their winding number. Arnold proposed a much deeper plan of study and introduced three invariants that are locally constant on generic immersions, i.e. curves where all self-intersections are transverse double points. We establish a bridge between the topological description of Arnold and the geometry of curves by investigating planar versions of knot energies. We prove existence of minimizers of a truncated version of the tangent-point energy for curves with fixed Arnold invariants and fixed winding number. By sending the truncation parameter to zero, we obtain a C^1-curve as the limit of a sequence of minimizers, and we investigate properties of that limit curve. An application of the principle of symmetric criticality by Palais yields the existence of point symmetric curves in the class of figure-eight shaped curves as critical points of the considered energy.
If you want to take part via Zoom please ask Prof. Frauenfelder for login details: Urs.Frauenfelder@math.uni-augsburg.de |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Urs Frauenfelder |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).