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Self‐repulsiveness of energies for closed submanifolds

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  • Jun O'Hara

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.

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  • Jun O'Hara, 2023. "Self‐repulsiveness of energies for closed submanifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 296(2), pages 797-810, February.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:2:p:797-810
    DOI: 10.1002/mana.202000158
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    1. Jun O'Hara & Gil Solanes, 2018. "Regularized Riesz energies of submanifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 291(8-9), pages 1356-1373, June.
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    1. Jun O'Hara & Gil Solanes, 2020. "Erratum to the paper “Regularized Riesz energies of submanifolds”: (Published in Math. Nachr. 291 (2018), no. 8–9, 1356–1373)," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 1014-1019, May.

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