Giacomo Vianello

collaborators

4 papers

math.CA2026

Plateau's Problem for intrinsic graphs in the Heisenberg Group

Roberto Monti, Giacomo Vianello

Using a geometric construction, we solve Plateau's Problem in the Heisenberg group $H^{1}$ for intrinsic graphs defined on a convex domain $D$ , under a smallness condition…

math.AP2026

Minimality of free-boundary axial hyperplanes in high dimensional circular cones via calibration

Giacomo Vianello

Consider an $(n + 1)$ -dimensional circular cone with opening angle $I^\pm \in (0, I ¨ )$ . Using a free-boundary adaptation of the classical calibration method, we prove that, for $n \geq 4$ …

math.AP2025

Stability of axial free-boundary hyperplanes in circular cones

Gian Paolo Leonardi, Giacomo Vianello

Given an axially-symmetric, $(n + 1)$ -dimensional convex cone $I^c ◯ \subset R^{n + 1}$ , we study the stability of the free-boundary minimal surface $I^£$ obtained by intersecting…

math.CA2025

Free-Boundary Monotonicity for Almost-Minimizers of the Relative Perimeter

Gian Paolo Leonardi, Giacomo Vianello

Let $E \subset I^c ◯$ be a local almost-minimizer of the relative perimeter in the open set $I^c ◯ \subset R^{n}$ . We prove a free-boundary monotonicity inequality for $E$ at a p…