11 papers
Carleman estimates for stationary -valued maps: a variational approach
Aria Halavati, Luca Spolaor
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizi…
Fine structure of the two-phase Bernoulli free boundaries in 2D
Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov
We prove that the branching set of a solution to a two-dimensional two-phase Bernoulli problem with constant coefficients is locally finite. We do this via a Weierstrass representa…
Stationary and stable varifolds with singularities
Camillo De Lellis, Jonas Hirsch, Luca Spolaor
We construct minimal -dimensional immersions in , equipped with a metric, , with a sequence of \emph{catenoidal necks} or \emph{floating disks…
Area minimizing hypersurfaces modulo : a geometric free-boundary problem
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
We consider area minimizing -dimensional currents in complete Riemannian manifolds of dimension . For odd moduli we prove that, away from a clo…
Measure of the singular set for -valued stationary hypercurrents
Jonas Hirsch, Luca Spolaor
We prove that the singular set of a multiplicity integral hypercurrent that is stationary in the sense of varifolds has a singular set of measure zero.
Structure of two-dimensional mod area-minimizing currents near flat singularities: the codimension one case
Anna Skorobogatova, Luca Spolaor, Salvatore Stuvard
We obtain a fine structural result for two-dimensional mod area-minimizing currents of codimension one, close to flat singularities. Precisely, we show that, locally around an…