Papers by Ignace Aristide Minlend
ESAIM: Control, Optimisation and Calculus of Variations
We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hyp... more We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of smooth branches of multiply-periodic hypersurfaces bifurcating from suitable parallel hyperplanes.
Archiv der Mathematik
Let (M, g) be a smooth compact Riemannian manifold of dimension N ≥ 2. We prove the existence of ... more Let (M, g) be a smooth compact Riemannian manifold of dimension N ≥ 2. We prove the existence of a family (Ω ε) ε∈(0,ε0) of self-Cheeger sets in (M, g). The domains Ω ε ⊂ M are perturbations of geodesic balls of radius ε centered at p ∈ M, and in particular, if p 0 is a non-degenerate critical point of the scalar curvature of g, then the family (∂Ω ε) ε∈(0,ε0) constitutes a smooth foliation of a neighborhood of p 0 .
Advances in Calculus of Variations, 2014
Let (M, g) be a compact Riemannian manifold of dimension N , N ≥ 2. In this paper, we prove that ... more Let (M, g) be a compact Riemannian manifold of dimension N , N ≥ 2. In this paper, we prove that there exists a family of domains (Ω ε ) ε∈(0,ε0) and functions u ε such that where ν ε is the unit outer normal of ∂Ω ε . The domains Ω ε are smooth perturbations of geodesic balls of radius ε. If, in addition, p 0 is a non-degenerate critical point of the scalar curvature of g then, the family (∂Ω ε ) ε∈(0,ε0) constitutes a smooth foliation of a neighborhood of p 0 . By considering a family of domains Ω ε in which (0.1) is satisfied, we also prove that if this family converges to some point p 0 in a suitable sense as ε → 0, then p 0 is a critical point of the scalar curvature. A Taylor expansion of he energy rigidity for the torsion problem is also given.
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Papers by Ignace Aristide Minlend