46 citations · 58 across the 5 of their papers we have counts for
6 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…
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…
Minimal clusters of four planar regions with the same area
Emanuele Paolini, Andrea Tamagnini
We prove that the optimal way to enclose and separate four planar regions with equal area using the less possible perimeter requires all regions to be connected. Moreover, the topo…
Structure of metric cycles and normal one-dimensional currents
Emanuele Paolini, Eugene Stepanov
We prove that every one-dimensional real Ambrosio-Kirchheim normal current in a Polish (i.e. complete separable metric) space can be naturally represented as an integral of simpler…
Decomposition of acyclic normal currents in a metric space
Emanuele Paolini, Eugene Stepanov
We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing…