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Nearly 20 years ago!
Energy of knots
Where is the ``best place'' to locate a street light?
(Nov 2018)
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Jun O'Hara (Wiki)
Professor. Room 309, Science Building 1
Department of Mathematics and Informatics,Faculty of Science, Chiba University
1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan
Notice: If the link is broken, it would be appreciated if you could let me know.
Research Interests: (see Research)
Geometric knot thoery, in particular, Knot energies (Wiki) including Möbius energy (Wiki). Movies of knots evolving themselves to decrease the energy are available on web. Youtube by Rob Scharein (the creator of KnotPlot), by Kazushi Ahara, a site by John Sullivan. One hour presentation file
Möbius Geometry of curves and surfaces (with Remi Langevin), one hour presentation file
Regularization of Riesz potential and energy of submanifolds (with Gil Solanes), residues of manifolds, generalized centers, and application to integral geometry, one hour presentation file
Topology of the spaces of knots (Configuration space of equilateral and equiangular hexagons) and linkages
Magnitude of metric spaces
Papers:
(with Gil Solanes) Regularized Riesz energies of submanifolds, Math. Nachr. 291 (2018), 1356-1373.
Renormalization of potentials and generalized centers, Adv. Appl. Math. 48 (2012), 365-392, arXiv
(with Remi Langevin) Conformal arc-length as 1/2-dimensional length of the set of osculating circles, Comm. Math. Helv. 85 (2010) 273-312, arXiv
(with R. Langevin) Conformally invariant energies of knots, J. Institut Math. Jussieu 4 (2005), 219-280, arXiv
Family of energy functionals of knots, Topology Appl. 48 (1992), 147-161
Energy of a knot, Topology 30 (1991), 241-247
Preprints:
Magnitude function determines generic finite metric spaces, arXiv 2401.00786
Book:
Energy of knots and conformal geometry. Series on Knots and Everything Vol. 33, World Scientific, Singapore, 304 pages. ISBN 981-238-316-6, 2003, Errata updated Sept. 2018
Mini-Course:
17-28 Jun 2019, Summer Conference on Topology and its Applications, Biology, Analysis, Geometry, Energies, Links [bagel19]
Talks:
Current projects:
Regularization of Riesz energies (Brylinski's beta functions) of submanifolds, residues, and application to (integral) geometry
Magnitude of finite metric subspace of Euclidean spaces
``Extrinsic Conformal Geometry'' (with Remi Langevin) and 2nd edition of ``Energy of knots and conformal geometry''
Former Home Page at Tokyo Metropolitan University
Mathematical Reviews Author ID 632389