22 citations · 59 across the 32 of their papers we have counts for
11 papers · 1 filter
CR-invariant energy of Legendrian knots in the Heisenberg group
Yoshihiko Matsumoto, Jun O'Hara
We introduce an energy functional for Legendrian knots in the 3-dimensional Heisenberg group , which serves as a sub-Riemannian analog of the Möbius invariant knot ene…
Self-repulsiveness of energies for closed submanifolds
Jun O'Hara
We show that the regularized Riesz $\a$-energy for closed submanifolds in $\RR^n$ blows up as degenerates to have double points if $\a\le-2\dim M$. This gives theoretical f…
Conformal invariance of the writhe of a knot
R. Langevin, J. O'Hara
We give a new proof of an old theorem by Banchoff and White 1975 that claims that the writhe of a knot is conformally invariant.
Conformal dual of a quadruplet of points
Jun O'Hara
Let be a quadruplet of points in . We define a ``dual'' quadruplet of it in a conformal geometric way. We show that the dual of a dual quadruplet coi…
Measure of a 2-component link
Jun O'Hara
A two-component link produces a torus as the product of the component knots in a two-point configuration space of a three-sphere. This space can be identified with a cotangent bund…
Energy of knots and the infinitesimal cross ratio
Jun O'Hara
This is a survey article on two topics. The Energy E of knots can be obtained by generalizing an electrostatic energy of charged knots in order to produce optimal knots. It turns o…