Differential Geometry and Parametrization of 3D Knots

Renormalization of \(r^{\bullet}\)-potentials and generalized centers

speaker: Jun O'Hara (Tokio Metropolitan University)

abstract: We generalize Riesz potential of a compact domain in \(\large \mathbb{R}^{m}\) by introducing renormalization of an \(\large r^{\alpha-m}\)-potential for \(\large \alpha\le0\). It can be considered as generalization of dual volumes of convex bodies introduced by Lutwak. We then study the points that attain extreme values of the (renormalized) potentials, which can be considered as generalization of center of mass. We also show that only balls attain etreme values among bodied with the same volume. (This is a preliminary talk to my talk "Möbius invariant energies and average linking with circles'' (with Gil Solanes) at Knots and Links: from Form to Function (2 July - 8 July))

timetable:
Tue 28 Jun, 11:00 - 12:00, Aula Dini
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