22 citations · 59 across the 32 of their papers we have counts for
11 papers · 1 filter
Uniqueness of centers of nearly spherical bodies
Jun O'Hara
An $r^{\an}$-center of a compact body $\Om$ in an dimensional Euclidean space is a point that gives an extremal value of the regularized Riesz potential, which is the (Hadamard…
Residues of manifolds
Jun O'Hara
The Riesz -energy of a manifold is the integration of the distance between two points to the power over the product space . Considered as a function of a comp…
Möbius invariant metrics on the space of knots
Jun O'Hara
We give a condition for a function to produce a Möbius invariant weighted inner product on the tangent space of the space of knots, and show that some kind of Möbius invariant knot…
Regularization of self inductance
Jun O'Hara
We introduce several methods to define the self-inductance of a single loop as the regularization of divergent integrals which we obtain by applying Neumann (or Weber) formula for…
Characterization of balls by generalized Riesz energy
Jun O'Hara
We show that balls, circles and 2-spheres can be identified by generalized Riesz energy among compact submanifolds of the Euclidean space that are either closed or with codimension…
Regularized Riesz energies of submanifolds
Jun O'Hara, Gil Solanes
Given a closed submanifold, or a compact regular domain, in euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs…