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Your search keyword '"Jun O'Hara"' showing total 2 results
Start Over Author "Jun O'Hara" Topic 53a30 Topic mathematical analysis
2 results on '"Jun O'Hara"'

1. Möbius invariant energies and average linking with circles

Author

Jun O'Hara and Gil Solanes

Subjects
Pure mathematics, General Mathematics, Hyperbolic space, Mathematical analysis, 53A30, 53C65, Computer Science::Computational Geometry, Integral geometry, renormalization, Renormalization, Planar, symplectic form, Möbius geometry, Invariant (mathematics), Mathematics, integral geometry, knot energies
Abstract

We introduce a Mobius invariant energy associated to planar domains, as well as a generalization to space curves. This generalization is a Mobius version of Banchoff-Pohl's notion of area enclosed by a space curve. A relation with Gauss-Bonnet theorems for complete surfaces in hyperbolic space is also described.

Published
2015

2. Measure of a 2-component link

Author

Jun O'Hara

Subjects
Pure mathematics, Energy, General Mathematics, Mathematical analysis, 53A30, link, Clifford torus, Torus, Geometric Topology (math.GT), Mathematics::Geometric Topology, Symplectic vector space, Mathematics - Geometric Topology, symplectic measure, Grassmannian, Möbius geometry, 57M25, FOS: Mathematics, Cotangent bundle, 57M25, 53A30, Tautological one-form, pseudo-Riemannian geometry, Link (knot theory), Mathematics::Symplectic Geometry, Mathematics, Symplectic manifold
Abstract

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 bundle and also with an indefinite Grassmannian. We show that the integration of the absolute value of the canonical symplectic form is equal to the area of the torus with respect to the pseudo-Riemannian structure, and that it attains the minimum only at the "best" Hopf links., to appear in Tohoku Math. J

Published
2007

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