Related papers: Flat interior singularities for area almost-minimi…

We construct new examples of normal (metric) currents using inverse systems of cube complexes. For any $N\ge 2$ we provide examples of $N$-dimensional normal currents whose associated vector fields are simple, and whose supports are purely…

We construct area-minimizing submanifolds with fractal singular sets on compact Riemannian manifolds. Thus, we settle a conjecture by Almgren and our answer is sharp dimensionwise. Furthermore, we can prescribe arbitrarily the strata in the…

We recently constructed type-IIB compactifications to four dimensions depending on a single additional coordinate, where a five-form flux $\Phi$ on an internal torus leads to a constant string coupling. Supersymmetry is fully broken when…

This is an announcement of a series of upcoming works on boundary regularity for area minimizing currents, one of which is in collaboration with Reinaldo Resende. The setting we consider is that of an area minimizing current with a smooth…

We study quasiisometric embeddings between finite-dimensional CAT(0) cube complexes. More specifically, we introduce geometric branching conditions under which flats in the domain, not necessarily of top rank, are mapped within finite…

The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…

We study almost-minimizers of anisotropic surface energies defined by a H\"older continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers…

The Frenkel-Kontorova model describes how an infinite chain of atoms minimizes the total energy of the system when the energy takes into account the interaction of nearest neighbors as well as the interaction with an exterior environment.…

In 1974, Federer proved that all area-minimizing hypersurfaces on orientable manifolds were calibrated by weakly closed differential forms. However, in this manuscript, we prove the contrary in higher codimensions: calibrated…

Consider an $m$-dimensional area minimizing mod$(2Q)$ current $T$, with $Q\in\mathbb{N}$, inside a sufficiently regular Riemannian manifold of dimension $m + 1$. We show that the set of singular density-$Q$ points with a flat tangent cone…

We provide a rather complete description of the sharp regularity theory for a family of heterogeneous, two-phase variational free boundary problems, $\mathcal{J}_\gamma \to $ min, ruled by nonlinear, $p$-degenerate elliptic operators.…

We compare singular homology and homology via integral currents in metric spaces that are homeomorphic to smooth manifolds. For such spaces, we provide sufficient conditions that guarantee the existence of a surjective homomorphism from the…

We introduce a notion of non-local almost minimal boundaries similar to that introduced by Almgren in geometric measure theory. Extending methods developed recently for non-local minimal surfaces we prove that flat non-local almost minimal…

We focus our attention on the one dimensional scalar theories that result from dimensionally reducing the free scalar field theory in arbitrary d dimensions. As is well known, after integrating out the angular coordinates, the free scalar…

We consider sequences of maps from an $(n+m)$-dimensional domain into the $(n-1)$-sphere, which satisfy a natural $p$-energy growth, as $p$ approaches $n$ from below. We prove that, up to subsequences, the Jacobians of such maps converge in…

This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We…

We prove that 2 dimensional Integral currents (i.e. integer multiplicity 2 dimensional rectifiable currents) which are almost complex cycles in an almost complex manifold admitting locally a compatible symplectic form are smooth surfaces…

We associate to any compact semi-algebraic set $X \subset \mathbb R^n$ a chain complex of currents $S_\ast (X)$ generated by integration along semi-algebraic submanifolds and we analyze the corresponding homology groups. In particular, we…

Poincar\'e proved nonexistence of formal first integrals near a nonresonant singularity of analytic autonomous differential systems. In the resonant case with one zero eigenvalue and others nonresonant, there remains an open problem on…

Let $f_1$, $f_2$, and $f_3$ be holomorphic functions on a complex manifold and assume that the common zero set of the $f_j$ has maximal codimension, i.e., that it is a complete intersection. We prove that the iterated Mellin transform of…