181 citations · 3.2k across the 184 of their papers we have counts for
5 papers · 2 filters
Necklaces with interacting beads: isoperimetric problems
Pavel Exner
We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places identical point charges at a closed curve at the…
Inequalities for means of chords, with application to isoperimetric problems
Pavel Exner, Evans M. Harrell, Michael Loss
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in with an attractive interaction supported on a clos…
Approximations of permutation-symmetric vertex couplings in quantum graphs
Pavel Exner, Ondrej Turek
We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such condition…
Spectrum of the Schrödinger operator in a perturbed periodically twisted tube
Pavel Exner, Hynek Kovařík
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowin…
An isoperimetric problem for leaky loops and related mean-chord inequalities
Pavel Exner
We consider a class of Hamiltonians in with attractive interaction supported by piecewise smooth loops of a fixed length , formally given by w…