Displaying similar documents to “The Nash-Kuiper process for curves”

Isometric immersions and induced geometric structures

D‘Ambra, G.

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In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.

Piecewise Convex Curves and their Integral Representation

Nedelcheva, M. D. (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 52A10. A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the...