Camillo De Lellis

activity

20242026

collaborators

11 papers

math.AP2026

Level sets of fractional Sobolev functions

Camillo De Lellis, Ming-Yuan Chang, Svitlana Mayboroda

We prove a coarea-type result for scalar functions $f$ in fractional Sobolev spaces $W^{s, p} (I^c ◯)$ with $I^c ◯ \subset R^{n}$ , $0 < s < 1$ , and $1 \leq p < \infty$ . Our theorem shows…

math.DG2026

Stationary and stable varifolds with singularities

Camillo De Lellis, Jonas Hirsch, Luca Spolaor

We construct minimal $m$ -dimensional immersions in $R^{m + 1}$ , equipped with a $C^{1, I^\pm}$ metric, $I^\pm \in [0, 1)$ , with a sequence of \emph{catenoidal necks} or \emph{floating disks…

math.AP2026

Some rigorous remarks on Migdal's momentum loop equation

BruÃ¨ Elia, Camillo De Lellis

We give a rigorous mathematical treatment of some portions of the theory developed by Alexander Migdal on the momentum loop equation.

math.AP2026

Regularity thresholds for anomalous dissipation and related phenomena in passive scalars

Marco Bagnara, Daniel W. Boutros, Camillo De Lellis +1

We prove the absence of anomalous dissipation for passive scalars driven by some random autonomous divergence-free vector fields in $T^{d}$ . In dimension $d = 2$ we just need c…

math.AP2025

Area minimizing hypersurfaces modulo $p$ : a geometric free-boundary problem

Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2

We consider area minimizing $m$ -dimensional currents $mod (p)$ in complete $C^{2}$ Riemannian manifolds $I^£$ of dimension $m + 1$ . For odd moduli we prove that, away from a clo…

math.AP2025

The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points

Camillo De Lellis, Anna Skorobogatova

We consider an area-minimizing integral current of dimension $m$ and codimension at least $2$ and fix an arbitrary interior singular point $q$ where at least one tangent cone is fl…

Level sets of fractional Sobolev functions

Stationary and stable varifolds with singularities

Some rigorous remarks on Migdal's momentum loop equation

Regularity thresholds for anomalous dissipation and related phenomena in passive scalars

Area minimizing hypersurfaces modulo p: a geometric free-boundary problem

The fine structure of the singular set of area-minimizing integral currents I: the singularity degree of flat singular points

Area minimizing hypersurfaces modulo $p$ : a geometric free-boundary problem