We prove that C∞ curves of constant curvature satisfy, in the sense of Gromov, the relative C-dense h-principle in the space of immersed curves in Euclidean space Rn≥3. In particular, in the isotopy class of any given C knot f there exists a C∞ knot e f of constant curvature which is C-close to f . More importantly, we show that if f is C, then the curvature of e f may be set equal to any const...

The sine-Gordon equation with periodic boundary conditions describes integrable dynamics on the space of closed curves of constant torsion, for which multi-phase solutions provide large classes of canonical knot representatives. In this letter we discuss the use of Bäcklund transformations for studying the topological properties and symmetries of multi-phase solutions and of their homoclinic ma...

The Griiths formalism is applied to nd constant torsion curves which are extremal for arclength with respect to variations preserving torsion, xing the endpoints and the binormals at the endpoints. The critical curves are elastic rods of constant torsion, which are shown to not realize certain boundary conditions. In the calculus of variations under nonholonomic constraints, one tries to nd the...

A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a " cutoff identification " which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, s...

in this note we review a simple criterion, due to ekedahl, for superspecial curves defined over finite fields.using this we generalize and give some simple proofs for some well-known superspecial curves.