3 citations · 5 across the 9 of their papers we have counts for
12 papers
A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group
A. Cesaroni, M. Novaga, P. Pozzi
The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement sch…
The rhombic dodecahedral conjecture
Annalisa Cesaroni, Matteo Novaga
We prove that every three-dimensional parallelohedron satisfies \[ \mathcal H^2(\partial P)\ge 12\sqrt2\,r(P)^2, \] where is the inradius of , with equality if and on…
The truncated octahedron minimizes surface area among parallelohedra of equal volume
Annalisa Cesaroni, Matteo Novaga
We prove that the regular truncated octahedron uniquely minimizes surface area among all parallelohedra of fixed volume. Equivalently, every three-dimensional parallelohedron s…
Local minimality of the truncated octahedron for the isoperimetric problem on parallelohedra
Annalisa Cesaroni, Matteo Novaga
We investigate the isoperimetric problem for the Voronoi cells of three-dimensional lattices. Using Selling parameters, we derive an explicit closed formula for the scale-invariant…
Non-local planelike minimizers and -convergence of periodic energies to a local anisotropic perimeter
Serena Dipierro, Matteo Novaga, Enrico Valdinoci +1
We investigate a homogenization problem related to a non-local interface energy with a periodic forcing term. We show the existence of planelike minimizers for such energy. Moreove…
A note on the honeycomb optimality among periodic convex tilings
Annalisa Cesaroni, Ilaria Fragalà, Matteo Novaga
We show that the hexagonal honeycomb is optimal among convex periodic tessellations of the plane, provided the cost functional is lower semicontinuous with respect to the Hausdorff…
Minimal periodic foams with fixed inradius
Annalisa Cesaroni, Matteo Novaga
In this note we show existence and regularity of periodic tilings of the Euclidean space into equal cells containing a ball of fixed radius, which minimize either the classical or…
Lattice tilings with minimal perimeter and unequal volumes
Francesco Nobili, Matteo Novaga
We study periodic tessellations of the Euclidean space with unequal cells arising from the minimization of perimeter functionals. Existence results and qualitative properties of mi…
Time-fractional Allen-Cahn equations versus powers of the mean curvature
Serena Dipierro, Matteo Novaga, Enrico Valdinoci
We show by a formal asymptotic expansion that level sets of solutions of a time-fractional Allen-Cahn equation evolve by a geometric flow whose normal velocity is a positive power…
Lattice tilings minimizing nonlocal perimeters
Annalisa Cesaroni, Ilaria Fragalà, Matteo Novaga
We prove the existence of periodic tessellations of minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement t…
A symmetry result for the Ornstein-Uhlenbeck operator
A. Cesaroni, M. Novaga, E. Valdinoci
In 1978 E. De Giorgi formulated a conjecture concerning the one-dimensional symmetry of bounded solutions to the elliptic equation Δu=F'(u), which are monotone in some direction. I…
Curvature flow in heterogeneous media
Annalisa Cesaroni, Matteo Novaga, Enrico Valdinoci
In recent years, there has been a growing interest in geometric evolution in heterogeneous media. Here we consider curvature driven fows of planar curves, with an additional space-…