Sobolev and isoperimetric inequalities for riemannian submanifolds

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The Calder\'on-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds (2014, unknown): “Indeed, according to [20], such a submanifold enjoys the L(1)-Sobolev inequality ‖u‖ m m−1 ≤ C(‖grad(u)‖1 + ‖u‖1), for every u ∈ Cc (M) and for some constant C > 0 depending on m and ‖H‖∞ < +∞.”
Stability properties and topology at infinity of $$f$$f-minimal hypersurfaces (2013, methodology): “Proof (Proof of Theorem 6)We follow the argument in [20,27].”
Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “The contributions to this field now constitute the corpus of a vast literature, which includes the papers [1, 4, 6, 10, 11, 15, 16, 20, 22, 24, 27, 31, 33, 39, 40, 45, 47, 49, 50, 52, 53, 54, 59, 60, 68, 89] and the monographs [17, 19, 21, 48, 67, 78].”
On the 1/H-flow by p-Laplace approximation: New estimates via fake distances under Ricci lower bounds (2019, background): “From [31, 32, 78, 77], this is equivalent to the existence, for each fixed o ∈ Ω, of a positive Green kernel  with pole at o, namely, of a positive distributional solution of Δp = − o on Ω: ∫Ω |∇|p−2⟨∇,∇ ⟩ = (o) ∀ ∈ Lipc(Ω).”