Strong approximation in h-mass of rectifiable currents under homological constraint - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Advances in Calculus of Variation Year : 2021

Strong approximation in h-mass of rectifiable currents under homological constraint

Abstract

Let h : R → R+ be a lower semi-continuous subbadditive and even function such that h(0) = 0 and h(θ) ≥ α|θ| for some α > 0. The h-mass of a k-polyhedral chain P =∑j θjσj in R n (0 ≤ k ≤ n) is defined as M h (P) := j h(θj) H k (σj). If T = τ (M, θ, ξ) is a k-rectifiable chain, the definition extends to M h (T) := M h(θ) dH k. Given such a rectifiable flat chain T with M h (T) < ∞ and ∂T polyhedral, we prove that for every η > 0, it decomposes as T = P + ∂V with P polyhedral, V rectifiable, M h (V) < η and M h (P) < M h (T) + η. In short, we have a polyhedral chain P which strongly approximates T in h-mass and preserves the homological constraint ∂P = ∂T. These results are motivated by the study of approximations of M h by smoother functionals but they also provide explicit formulas for the lower semicontinuous envelope of T → M h (T) + I ∂S (∂T) with respect to the topology of the flat norm.
Fichier principal
Vignette du fichier
Strong_approximation_in_h_mass_June11.pdf (505.52 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01813234 , version 1 (12-06-2018)

Identifiers

Cite

Antonin Chambolle, Luca Alberto Davide Ferrari, Benoît Merlet. Strong approximation in h-mass of rectifiable currents under homological constraint. Advances in Calculus of Variation, 2021, 14 (3), pp.343--363. ⟨10.1515/acv-2018-0079⟩. ⟨hal-01813234⟩
345 View
131 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More