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The behavior of special classes of isometric foldings of the Riemannian sphere $S^{2}$ under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding $f_{s}$ defined by $f_{s} (x, y, z) = (x, y, | z |)$ .

Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

A coordinate cone in $ℝ^{n}$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $ℝ^{n}$ , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

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...-Applications dans une variété

Approximating homotopy equivalences of surfaces by homeomorphisms

Deformation of Maps to Branched Coverings in Dimension Three.

Miller's theorem for cell-like embedding relations

On deformations of spherical isometric foldings

Semi-monotone sets

Simplexwise linear and piecewise linear near self-homeomorphisms of surfaces

Simplicial approximation of small multifunctions

Аппроксимация вложений многообразий в коразмерности единица

Аппроксимация компактов в E $^{n}$ в коразмерности, большей двух

О несуществовании локально-плоской аппроксимации в коразмерности два

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