EXISTENCE AND PROPERTIES OF CLOSED FREE P-ELASTIC CURVES - ALVARO PAMPANO (TEXAS TECH UNIVERSITY)
Abstract: The study of elastic curves (p=2) as well as their generalization to p-elastic curves is a central topic in differential geometry which goes back to the days of the Bernoulli family and L. Euler. In particular, free p-elastic curves (ie, critical points for compactly supported variations without constraining the length of the curves) arise in many different problems.
In the Euclidean plane, closed free p-elastic curves do not exist, but for a remarkable exception (namely, p=1). In the Euclidean sphere, the existence of closed free elastic curves (p=2) is well known. In this talk we show the existence of infinitely many closed free p-elastic curves for every 0<p<1, all of which are unstable. Using the theory of Killing vector fields along curves we will geometrically describe these curves and highlight an interesting evolution related to them.
This talk will be presented in a hybrid mode. It will take place at the Aula Seminari (3rd floor) of the Department of Mathematical Sciences "G. L. Lagrange" (Politecnico di Torino), Corso Duca degli Abruzzi 24.
We will send out the link to attend the talk remotely one day before the talk.
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