Nonlocal minimal surfaces: recent developments, applications, and future directions | SeMA
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Minimal surfaces in closed 3-manifolds are classically constructed via the Almgren-Pitts
approach. The Allen-Cahn approximation has proved to be a powerful alternative, and …

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length
constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness …

This article addresses the regularity issue for stationary or minimizing fractional harmonic
maps into spheres of order s ∈ (0, 1) s∈(0, 1) in arbitrary dimensions. It is shown that such …

Given a half-harmonic map $ u\in\dot H^{\frac {1}{2}, 2}(\mathbb {R},\mathbb {S}^ 1) $
minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb …

In this paper we consider sphere-valued stationary/minimizing fractional harmonic mappings
introduced in recent years by several authors, especially by Millot-Pegon-Schikorra\cite …

Let Σ Σ a closed nn‐dimensional manifold, N⊂ RM N⊂R^M be a closed manifold, and let
u∈ W s, ns (Σ, N) u∈W^s,ns(Σ,N) for s∈(0, 1) s∈(0,1). We extend the monumental work of …

In this article, we investigate sequences of discontinuous martingales on submanifolds of
higher-dimensional Euclidean space. Those sequences naturally arise when we deal with a …

This is the final report of the ANR project 14-CE25-0009-01 entitled “Mathematical Analysis
of Topological Singularities in some physical problems”(MAToS) that was developed by the …

Cette thèse est dédiée à l'étude de deux problèmes variationnels géométriques impliquant
des énergies non-locales: d'une part, la géométrie et les singularités des applications …