4 papers
Rearrangement inequalities for functionals with monotone integrands
Almut Burchard, Hichem Hajaiej
The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangeme…
On an isoperimetric inequality for a Schrodinger operator depending on the curvature of a loop
Almut Burchard, Lawrence E. Thomas
Let C be a smooth closed curve of length 2 Pi in R^3, and let k(s) be its curvature, regarded as a function of arc length. We associate with this curve the one-dimensional Schrodin…
On the Cauchy problem for a dynamical Euler's elastica
Almut Burchard, Lawrence E. Thomas
The dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation invol…
Hölder Regularity and Dimension Bounds for Random Curves
Michael Aizenman, Almut Burchard
Random systems of curves exhibiting fluctuating features on arbitrarily small scales () are often encountered in critical models. For such systems it is shown that scale-invaria…