ti sarei grata se potessi inoltrare l'annuncio del prossimo seminario MAP (di cui riporto sotto le informazioni) alla mailing list dei geometri, visto che lo speaker è Cristian Sopio, che so essere stato invitato in precedenza per un seminario di geometria.

Grazie mille,

Chiara

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In 1950, Milnor introduced a definition of total curvature for rectifiable (hence Lipschitz) curves in R^n and proved that if the curve is C^2-regular and parametrized by arc length, this definition coincides with the integral of the norm of the geodesic curvature of the curve. In 2023, Mucci and Saracco proposed a definition of p-curvature for any exponent p greater than or equal to 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 geodesic 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.