The gradient flow of O'Hara's knot energies

Simon Blatt

doi:10.1007/s00208-017-1540-4

The gradient flow of O'Hara's knot energies

Simon Blatt

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Jun O’Hara invented a family of knot energies E j, p, j, p ∈ (0, ∞), O’Hara in Topology Hawaii (Honolulu, HI, 1990). World Science Publication, River Edge 1992. We study the negative gradient flow of the sum of one of the energies Eα = Eα,1,α ∈ (2, 3), and a positive multiple of the length. Showing that the gradients of these
knot energies can be written as the normal part of a quasilinear operator, we derive
short time existence results for these flows. We then prove long time existence and
convergence to critical points.

Translated title of the contribution	The gradient flow of O'Hara's knot energies
Original language	English
Number of pages	69
Journal	MATHEMATISCHE ANNALEN
DOIs	https://doi.org/10.1007/s00208-017-1540-4
Publication status	Published - 2017

Bibliographical note

online first

Fields of Science and Technology Classification 2012

101 Mathematics

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10.1007/s00208-017-1540-4Licence: CC BY

Cite this

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The gradient flow of O'Hara's knot energies

Abstract

Bibliographical note

Fields of Science and Technology Classification 2012

Access to Document

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