Add to ORKGA knot energy is a real-valued function on a space of curves which in some sense assigns higher energy values to more complicated curves. The key property of any knot energy is self-repulsiveness: for a sequence of curves approaching a self-intersection, the energy blows up to infinity. While the study of optimally embedded curves as minimizers of energy among a given knot class has been well-documented, this thesis investigates the existence of optimally immersed self-intersecting curves. Because any self-intersecting curve will have infinite knot energy, parameter-dependent renormalizations of the energy remove the singular behavior of the curve. This process allows for the careful selection of an optimally immersed curve
The M\"obius energy is a well-studied knot energy with nice regularity and self-repulsive properties...
We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of clos...
In this article, we investigate regular curves whose derivatives have vanishing mean oscillations. W...
We study a two-point self-avoidance energy Eq which is defined for all rectifiable curves in Rn as t...
AbstractWe define a new class of knot energies (known as renormalization energies) and prove that a ...
We investigate knot-theoretic properties of geometrically defined curvature energies such as integra...
Probably the most natural energy functional to be considered for knotted strings is the one given by...
AbstractAn energy function is defined for C2 knots. It is shown that the function has several attrac...
In this article, we raise the question if curves of finite (j, p)-knot energy introduced by O’Hara a...
In this article we raise the question if curves of finite ( j, p)-knot energy intro-duced by O’H ar...
AbstractWe define energy functionals on the space of embeddings from S1 into R3 and show the finiten...
AbstractA knot is considered as an n-gon in R3. Two potential energies for these PL knot conformatio...
AbstractThe Möbius energy of a knot is an energy functional for smooth curves based on an idea of se...
The Möbius energy of a knot is an energy functional for smooth curves based on an idea of self-repel...
In this thesis, we examine the energy landscape of knot energies, trying to gain information about w...
The M\"obius energy is a well-studied knot energy with nice regularity and self-repulsive properties...
We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of clos...
In this article, we investigate regular curves whose derivatives have vanishing mean oscillations. W...
We study a two-point self-avoidance energy Eq which is defined for all rectifiable curves in Rn as t...
AbstractWe define a new class of knot energies (known as renormalization energies) and prove that a ...
We investigate knot-theoretic properties of geometrically defined curvature energies such as integra...
Probably the most natural energy functional to be considered for knotted strings is the one given by...
AbstractAn energy function is defined for C2 knots. It is shown that the function has several attrac...
In this article, we raise the question if curves of finite (j, p)-knot energy introduced by O’Hara a...
In this article we raise the question if curves of finite ( j, p)-knot energy intro-duced by O’H ar...
AbstractWe define energy functionals on the space of embeddings from S1 into R3 and show the finiten...
AbstractA knot is considered as an n-gon in R3. Two potential energies for these PL knot conformatio...
AbstractThe Möbius energy of a knot is an energy functional for smooth curves based on an idea of se...
The Möbius energy of a knot is an energy functional for smooth curves based on an idea of self-repel...
In this thesis, we examine the energy landscape of knot energies, trying to gain information about w...
The M\"obius energy is a well-studied knot energy with nice regularity and self-repulsive properties...
We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of clos...
In this article, we investigate regular curves whose derivatives have vanishing mean oscillations. W...