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

@article{Chambolle2019StrongAI,
  title={Strong approximation in h-mass of rectifiable currents under homological constraint},
  author={A. Chambolle and Luca Alberto Davide Ferrari and Beno{\^i}t Merlet},
  journal={Advances in Calculus of Variations},
  year={2019},
  volume={14},
  pages={343 - 363}
}
Abstract Let h : ℝ → ℝ + {h:\mathbb{R}\to\mathbb{R}_{+}} be a lower semicontinuous subbadditive and even function such that h ⁢ ( 0 ) = 0 {h(0)=0} and h ⁢ ( θ ) ≥ α ⁢ | θ | {h(\theta)\geq\alpha|\theta|} for some α > 0 {\alpha>0} . If T = τ ⁢ ( M , θ , ξ ) {T=\tau(M,\theta,\xi)} is a k-rectifiable chain, its h-mass is defined as 𝕄 h ⁢ ( T ) := ∫ M h ⁢ ( θ ) ⁢ 𝑑 ℋ k . \mathbb{M}_{h}(T):=\int_{M}h(\theta)\,d\mathcal{H}^{k}. Given such a rectifiable flat chain T with 𝕄 h ⁢ ( T ) < ∞ {\mathbb{M}_… 

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