Self-repulsiveness of energies for closed submanifolds

Abstract

We show that the regularized Riesz $\a$-energy for closed submanifolds $M$ in $\RR^n$ blows up as $M$ degenerates to have double points if $\a\le-2\dim M$. This gives theoretical foundation of numerical experiments to evolve surfaces to decrease the energy which have been carried out since 90's.

arXiv comment14 pages, two figures

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Cited by in corpus (1)

• M{ö}bius-invariant self-avoidance energies for non-smooth sets in arbitrary dimensions