22 citations · 59 across the 32 of their papers we have counts for
4 papers · 1 filter
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…
Strict power concavity of a convolution
Jun O'Hara, Shigehiro Sakata
We give a sufficient condition for the strict parabolic power concavity of the convolution in space variable of a function defined on and a functi…
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…
Pompeiu's theorem and the moduli space of triangles
Jun O'Hara
We introduce a kind of converse of Pompeiu's theorem. Fix an equilateral triangle , then for any triangle there is a unique point inside th…