“Weak elastic energy of rectifiable curves in the sphere”
Martedì 21 Aprile 2026, ore 11:30 - Sala Riunioni 7B1 - Cristian Sopio (Università di Parma)
Abstract
In 1950, Milnor introduced a definition of Total Curvature for rectifiable curves in $\mathbb{R}^n$. In 2023, Mucci and Saracco proposed a definition of $p$-curvature for any exponent $p \geq 1$, showing that a rectifiable curve parametrized by arc length belongs to the Sobolev space $W^{2,p}$ if and only if its $p$-curvature is finite. Moreover, in this case, the $p$-curvature equals the integral on the curve of the $p$-th power of the norm of its curvature. In this seminar, I will explain how the concept of $p$-curvature can be extended to rectifiable curves in the sphere and how analogous results can be obtained in this setting.
This is joint work with D. Mucci and A. Saracco.
