Topology of sobolev mappings, II

By Fengbo Hang, F. Lin. 2003

125 citations recorded by the source corpus.

This paper addresses some topological and analytical issues concern- ing Sobolev mappings between compact Riemannian manifolds. Among the results we obtained are unified proofs of various generalizations of results obtained in a recent work of Brezis and Li. In particular we solved two conjectures in (BL). We also give a topological obstruction for the weak sequential density of smooth maps in a given Sobolev mapping space. Finally we show a necessary and suf- ficient topological condition under which the smooth maps are strongly dense in the Sobolev spaces. The earlier result, Theorem 1 of (B2), was shown to be not correct.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d47b7f2cf31f4a9194a192200a1a35abba7b4c9d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Orientability and Energy Minimization in Liquid Crystal Models (2010, background): “f the manifold with boundary (see the discussion in the Appendix for more details). In the rest of the paper an open and connected set is called a domain. Let us deﬁne, in a standard manner (see also [16] and the references there) the Sobolev spaces W1,p(M,N) where Mis a C0 manifold and Nis a smooth”
Sobolev Mappings between Manifolds and Metric Spaces (2009, background): “This, however, turned out to be false: Hang and Lin [38] provided a counterexample to Bethuel’s claim by demonstrating that despite the equality π3(CIP2) = 0, C∞(CIP3, CIP2) is not dense in W 1,3(CIP3, CIP2).”
Q-valued functions revisited (2008, background): “em of whether or not general Sobolev mappings can be approximated with Lipschitz ones is a very subtle issue already when the target is a smooth Riemannian manifold (see for instance [SU82], [Bet91], [HL03] and [HR07]). The truncation technique is, instead, valid in a much more general setting, see ”