46 citations · 89 across the 18 of their papers we have counts for
22 papers
On the Steiner tree connecting a fractal set
Emanuele Paolini, Eugene Stepanov
We construct an example of an infinite planar embedded self-similar binary tree which is the essentially unique solution to the Steiner problem of finding the shortest connecti…
Isoperimetric planar clusters with infinitely many regions
Matteo Novaga, Emanuele Paolini, Eugene Stepanov +1
An infinite cluster in is a sequence of disjoint measurable sets , , called regions of the cluster. Given the volu…
Constructive controllability for incompressible vector fields
Sergey Kryzhevich, Eugene Stepanov
We give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e.\ incompressible) vect…
Infinite multidimensional scaling for metric measure spaces
Alexey Kroshnin, Eugene Stepanov, Dario Trevisan
For a given metric measure space we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimen…
Isoperimetric clusters in homogeneous spaces via concentration compactness
Matteo Novaga, Emanuele Paolini, Eugene Stepanov +1
We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous…
On exterior differential systems involving differentials of Hölder functions
Eugene Stepanov, Dario Trevisan
We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional…