Topology of Sobolev Mappings
Fengbo Hang, Fanghua Lin · Mathematical Research Letters · 2001
This paper addresses some topological and analytical issues concerning 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 sufficient 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.