6 papers
Anisotropic isoperimetric double tilings of the plane
Francesco Nobili, Matteo Novaga, Emanuele Paolini
We study periodic partitions of the plane into two distinct cells minimizing the anisotropic -perimeter. For a rectangular lattice , we compute explicitly the $(G,\ell_1…
Optimal sets for a geometric oscillation energy
Matteo Novaga, Fumihiko Onoue, Emanuele Paolini
We investigate the nonlocal energy corresponding to the -oscillation of the unit normal vector for hypersurfaces, or the unit tangent vector for curves. The energy satisfies geo…
Periodic double tilings of the plane
Francesco Nobili, Matteo Novaga, Emanuele Paolini
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e.,…
Existence of a non-standard isoperimetric triple partition
Matteo Novaga, Emanuele Paolini, Vincenzo Maria Tortorelli
We show existence of a isoperimetric -partition of , with one set of finite volume and two of infinite volume, which is asymptotic to a singular minimal cone.
On the total surface area of potato packings
Matteo Novaga, Emanuele Paolini, Eugene Stepanov
We prove that if we fill without gaps a bag with infinitely many potatoes, in such a way that they touch each other in few points, then the total surface area of the potatoes must…
Steiner trees with infinitely many terminals on the sides of an angle
Danila Cherkashin, Emanuele Paolini, Yana Teplitskaya
The Euclidean Steiner problem is the problem of finding a set , with the shortest length, such that is connected, where is a given set in a Euclidean space. The…