3 papers
math.AP2019
Variational formulae and estimates of O'Hara's knot energies
Shoya Kawakami, Takeyuki Nagasawa
O'Hara's energies, introduced by Jun O'Hara, were proposed to answer the question of what is the canonical shape in a given knot type, and were configured so that the less the ener…
math.AP2019
Recent topics on the O'Hara energies
Shoya Kawakami
The O'Hara energies, introduced by Jun O'Hara in 1991, were proposed to answer the question of what is a "good" figure in a given knot type. A property of the O'Hara energies is th…
math.NA2019
A discretization of O'Hara's knot energy and its convergence
Shoya Kawakami
In this paper, we propose a discrete version of O'Hara's knot energy defined on polygons embedded in the Euclid space. It is shown that values of the discrete energy of polygons in…