Fractional Isoperimetric Noether's Theorem in the Riemann–Liouville Sense

Fractional Optimal Control in the Sense of Caputo and the Fractional Noether’s Theorem

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal’s necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using Agrawal’s Euler-Lagrange equation and the Lagrange multiplier technique, we obtain here a Noether-like theorem for fractional optimal control problems in the se...

An isoperimetric comparison theorem

An Isoperimetric Theorem in Plane Geometry

An isoperimetric theorem in plane geometry Alan Siegel1 COURANT INSTITUTE OF MATHEMATICAL SCIENCES NEW YORK UNIVERSITY New York Abstract Let be a simple polygon. Let the vertices of be mapped, according to a counterclockwise traversal of the boundary, into a strictly increasing sequence of real numbers in . Let a ray be drawn from each vertex so that the angle formed by the ray and a horizontal...

A Quantitative Isoperimetric Inequality for Fractional Perimeters

Recently Frank & Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.

Fractional Isoperimetric Inequalities and Subgroup Distortion

Isoperimetric inequalities measure the complexity of the word problem in finitely presented groups by giving a bound on the number of relators that one must apply in order to show that a word w in the given generators represents the identity. Such bounds are given in terms of the length of w, and the function describing the optimal bound is known as the Dehn function of the group. (Modulo a sta...