AbstractThe Möbius energy of a knot is an energy functional for smooth curves based on an idea of self-repelling. If a knot has a thick tubular neighborhood, we would intuitively expect the energy to be low. In this paper, we give explicit bounds for energy in terms of the ropelength of the knot, i.e., the ratio of the length of a thickest tube to its radius
The Newtonian energy EN of an object is defined by the energy required to charge a conductive object...
AbstractWe establish a new relationship between total curvature of knots and crossing number. If K i...
Probably the most natural energy functional to be considered for knotted strings is the one given by...
The Möbius energy of a knot is an energy functional for smooth curves based on an idea of self-repel...
In this paper we define a set of radii called thickness for simple closed curves denoted by K, which...
This paper considers and relates several notions of energy and other measures of geometric complexit...
AbstractGiven a “short” piece of rope, one can tie only “simple” knots. We make this precise by mode...
Energy minimizing smooth knot configurations have long been approximated by finding knotted polygons...
AbstractAn energy function is defined for C2 knots. It is shown that the function has several attrac...
We investigate knot-theoretic properties of geometrically defined curvature energies such as integra...
New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are def...
Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a ...
We establish a fundamental connection between smooth and polygonal knot energies, showing that the M...
AbstractWe define a new class of knot energies (known as renormalization energies) and prove that a ...
We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of clos...
The Newtonian energy EN of an object is defined by the energy required to charge a conductive object...
AbstractWe establish a new relationship between total curvature of knots and crossing number. If K i...
Probably the most natural energy functional to be considered for knotted strings is the one given by...
The Möbius energy of a knot is an energy functional for smooth curves based on an idea of self-repel...
In this paper we define a set of radii called thickness for simple closed curves denoted by K, which...
This paper considers and relates several notions of energy and other measures of geometric complexit...
AbstractGiven a “short” piece of rope, one can tie only “simple” knots. We make this precise by mode...
Energy minimizing smooth knot configurations have long been approximated by finding knotted polygons...
AbstractAn energy function is defined for C2 knots. It is shown that the function has several attrac...
We investigate knot-theoretic properties of geometrically defined curvature energies such as integra...
New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are def...
Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a ...
We establish a fundamental connection between smooth and polygonal knot energies, showing that the M...
AbstractWe define a new class of knot energies (known as renormalization energies) and prove that a ...
We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of clos...
The Newtonian energy EN of an object is defined by the energy required to charge a conductive object...
AbstractWe establish a new relationship between total curvature of knots and crossing number. If K i...
Probably the most natural energy functional to be considered for knotted strings is the one given by...
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