Self‐repulsiveness of energies for closed submanifolds

Jun O'Hara

Mathematische Nachrichten, 2023, vol. 296, issue 2, 797-810

Abstract: We show that the regularized Riesz α‐energy for smooth closed submanifolds M in Rn$\mathbb {R}^n$ blows up as M degenerates to have double points if α≤−2dimM$\alpha \le -2\dim M$. This gives theoretical foundation of numerical experiments to evolve surfaces to decrease the energy that have been carried out since the 90's.

Date: 2023
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