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A geometric theory of harmonic and semi-conformal maps

Anders Kock (2004)

Open Mathematics

We describe for any Riemannian manifold M a certain scheme M L, lying in between the first and second neighbourhood of the diagonal of M. Semi-conformal maps between Riemannian manifolds are then analyzed as those maps that preserve M L; harmonic maps are analyzed as those that preserve the (Levi-Civita-) mirror image formation inside M L.

Ambiguous loci of the farthest distance mapping from compact convex sets

F. De Blasi, J. Myjak (1995)

Studia Mathematica

Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by K 0 the set of all X ∈ K() such that the farthest distance mapping a M X ( a ) is multivalued on a dense subset of . It is proved that K 0 is a residual dense subset of K().

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