Giacomo Vianello

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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…