Topology of Sobolev mappings

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Topology of sobolev mappings, II (2003, unknown): “This is a sequel to [6, 7, 8].”
On the Sobolev Space of Isometric Immersions (2004, background): “The respective topologies of M and N and Integer part of p determine whether smooth maps are dense in this space [3], [4], [12], [29] and [13].”
Orientability and Energy Minimization in Liquid Crystal Models (2010, background): “Let us define, in a standard manner (see also [19] and the references there) the Sobolev spaces W (M,N) where M is a C manifold and N is a smooth manifold isometrically embedded in R: W (M,N) = {f : f ∈ W (M,R), f(x) ∈ N, a.”
Local Minimizers and Quasiconvexity – the Impact of Topology (2005, background): “This together with Theorem 1.1 in [ 38 ] implies that u (j ) and u (∞) lie in the same path-connected component of W 1,p (X , Y).”
Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces (2001, background): “In particular, one may ask whether X is path-connected and whether C∞(Ω;S1) is dense in X .”
Sobolev Mappings between Manifolds and Metric Spaces (2009, background): “We do not discuss this topic here and refer the reader to [26, 36, 37, 39, 40, 66, 67].”
Weak density of smooth maps for the Dirichlet energy between manifolds (2003, background): “Lin [ HaL1 ] showed that one should be careful while considering a generic smooth compact manifold M as the domain.”