Related papers: Minimal periodic foams with equal cells

Real foams can be viewed as a geometrically well-organized dispersion of more or less spherical bubbles in a liquid. When the foam is so drained that the liquid content significantly decreases, the bubbles become polyhedral-like and the…

The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.

We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Riemannian metric is compact.

We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.

Tropical polyhedra are known to be representable externally, as intersections of finitely many tropical half-spaces. However, unlike in the classical case, the extreme rays of their polar cones provide external representations containing in…

We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of…

We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius. We illustrate it by obtaining some…

In this paper we prove existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in $\mathbb R^3$. In particular, we obtain these surfaces…

In this paper, we show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic $3$-manifolds except some special cases.

Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global $\frac{1}{n+1}$-H\"older continuous in time mean curvature flow with mobilities of a bounded anisotropic partition in any dimension using the…

We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth $3$-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at…

We study various regularity properties of minimizers of the $\Phi$--perimeter, where $\Phi$ is a norm. Under suitable assumptions on $\Phi$ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is…

It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the orientable and smooth category, we determine the smallest possible $m$ when $n\geq 3g$.…

We prove several results relating the nonvanishing and the existence of good minimal models of different pairs that have the same underlying variety.

We prove the existence of a 2-dimensional nonaspherical simply connected cell-like Peano continuum (the space itself was constructed in one of our earlier papers). We also indicate some relations between this space and the well-known…

We identify quotient polynomial rings isomorphic to the recently found fundamental fusion algebras of logarithmic minimal models.

In this paper, we prove that the $3$-sphere endowed with an arbitrary Riemannian metric either contains at least two embedded minimal $2$-spheres or admits an optimal foliation by $2$-spheres. This generalizes recent results by…

This paper proposes a connection between algebraic K-theory and foam cobordisms, where foams are stratified manifolds with singularities of a prescribed form. We consider $n$-dimensional foams equipped with a flat bundle of…

In this paper we prove the connectedness of isoperiodic moduli spaces of meromorphic differentials with at least three simple poles on homologically marked smooth curves whose periods are either not contained in a real line, or not…

We prove the existence of a one parameter family of minimal embedded hypersurfaces in $R^{n+1}$, for $n \geq 3$, which generalize the well known 2 dimensional "Riemann minimal surfaces". The hypersurfaces we obtain are complete, embedded,…