**abstract:**
Given a boundary curve in \mathbb{R}^{3,} uniqueness of the
minimizing surface is known only under very restrictive assumptions
and many examples have been provided of curves admitting different
minimizers. In the late seventies, Morgan proved under specific
conditions that almost every curve is the boundary of a unique
area-minimizing surface, showing that uniqueness is a \emph{generic}
property. Relying on a recent boundary regularity theorem proved by De
Lellis, De Philippis, Hirsch and Massaccesi, I will explain how it is
possible to extend Morgan's result to full generality, \emph{i.e.} to
general ambient manifolds of any dimension, to any codimension and
with no assumptions on the geometry of the boundary. The argument of
the proof also delivers generic absence of two-sided boundary points
and generic multiplicity one of area-minimizing integral currents. If
time permits, I will also explain how to prove generic uniqueness for
a Plateau-type problem studied in optimal transport, providing a
strategy that may have a number of other applications. The talk is
based on a joint study with A. Marchese, A. Merlo and S.
Steinbruechel.

Wed 20 Sep, 17:20 - 18:20, Aula Dini

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