26 citations · 130 across the 22 of their papers we have counts for
24 papers
The Brakke-BV structure of flat flows
Daniele De Gennaro, Salvatore Stuvard
We show that, in ambient dimension at most seven, varifold limits of the minimizing movements scheme introduced by Almgren--Taylor--Wang and Luckhaus--Sturzenhecker are integral Br…
The epsilon-regularity theorem for Brakke flows near triple junctions
Salvatore Stuvard, Yoshihiro Tonegawa
We establish the -regularity theorem for -dimensional, possibly forced, Brakke flows near a static, multiplicity-one triple junction. This result provides the parab…
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…
Classical solutions to the soap film capillarity problem for plane boundaries
Giulia Bevilacqua, Salvatore Stuvard, Bozhidar Velichkov
We study the soap film capillarity problem, in which soap films are modeled as sets of least perimeter among those having prescribed (small) volume and satisfying a topological spa…
New advances on the existence and regularity of Brakke's mean curvature flows
Salvatore Stuvard
In this survey paper, I discuss some recent progress on the existence and regularity of Brakke flows. These include: an "end-time version" of Brakke's local regularity theorem, whi…
Excess decay for minimizing hypercurrents mod
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
We consider codimension area-minimizing -dimensional currents mod an even integer in a Riemannian submanifold of the Euclidean space. We prove a suitabl…
End-time regularity theorem for Brakke flows
Salvatore Stuvard, Yoshihiro Tonegawa
For a general -dimensional Brakke flow in locally close to a -dimensional plane in the sense of measure, it is proved that the flow is represented locally as a…
Fine structure of the singular set of area minimizing hypersurfaces modulo
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
Consider an area minimizing current modulo of dimension in a smooth Riemannian manifold of dimension . We prove that its interior singular set is, up to a relatively c…
On the existence of canonical multi-phase Brakke flows
Salvatore Stuvard, Yoshihiro Tonegawa
This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is a Brakke flow and a…
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 clos…
Dynamical instability of minimal surfaces at flat singular points
Salvatore Stuvard, Yoshihiro Tonegawa
Suppose that a countably -rectifiable set is the support of a multiplicity-one stationary varifold in with a point admitting a flat tangent plane of…
Smoothness of collapsed regions in a capillarity model for soap films
Darren King, Francesco Maggi, Salvatore Stuvard
We study generalized minimizers in the soap film capillarity model introduced in [arXiv:1807.05200,arXiv:1907.00551]. Collapsed regions of generalized minimizers are shown to be sm…
Collapsing and the convex hull property in a soap film capillarity model
Darren King, Francesco Maggi, Salvatore Stuvard
Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume…
An existence theorem for Brakke flow with fixed boundary conditions
Salvatore Stuvard, Yoshihiro Tonegawa
Consider an arbitrary closed, countably -rectifiable set in a strictly convex -dimensional domain, and suppose that the set has finite -dimensional Hausdorff measure a…
Regularity of area minimizing currents mod
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +1
We establish a first general partial regularity theorem for area minimizing currents , for every , in any dimension and codimension. More precisely, we prove th…
Area minimizing currents mod : linear regularity theory
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +1
We establish a theory of -valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently a…
Plateau's problem as a singular limit of capillarity problems
Darren King, Francesco Maggi, Salvatore Stuvard
Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning conditi…
A multi-material transport problem with arbitrary marginals
Andrea Marchese, Annalisa Massaccesi, Salvatore Stuvard +1
In this paper we study general transportation problems in , in which different goods are moved simultaneously. The initial and final positions of the goods are pr…
Soap films with gravity and almost-minimal surfaces
Francesco Maggi, Antonello Scardicchio, Salvatore Stuvard
Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvat…
Rectifiability of the singular set of multiple valued energy minimizing harmonic maps
Jonas Hirsch, Salvatore Stuvard, Daniele Valtorta
In this paper we study the singular set of Dirichlet-minimizing -valued maps from into a smooth compact manifold without boundary. Similarly to what…
Multiple valued sections of vector bundles: the reparametrization theorem for -valued functions revisited
Salvatore Stuvard
We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some usefu…
On the lower semicontinuous envelope of functionals defined on polyhedral chains
Maria Colombo, Antonio De Rosa, Andrea Marchese +1
In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by $H \colon \mathbb…
Multiple valued Jacobi fields
Salvatore Stuvard
We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold of a Riemannian manifold . We define the mu…
On the structure of flat chains modulo
Andrea Marchese, Salvatore Stuvard
In this paper, we prove that every equivalence class in the quotient group of integral -currents modulo in Euclidean space contains an integral current, with quantitative es…