Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen

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A literature survey of low‐rank tensor approximation techniques (2013, neutral): “As for the TT decomposition, the set of tensors having fixed HT-rank forms a smooth manifold [84, 256, 257].”
Low-rank tensor completion by Riemannian optimization (2014, methodology): “Hence, the chain rule yields the smoothness of the operator PHOr on D. 2.2 Manifold setting The set Mr of tensors of fixed multilinear rank r = (r1, r2, . . . , rd) forms a smooth embedded submanifold of Rn1×···×nd [28, 29].”
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces (2014, background): “The problem is related to the deeper fact that C≤r is not closed for d ≥ 3 and r ≥ 2 [50], that is, the infimum in (5) is typically not attained.”