Affine isoperimetric inequalities for piecewise linear surfaces

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This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give upper and lower bounds for the minimal number of triangles needed to forma triangulated embedded orientable surface in R^d having P as its geometric boundary. The most interesting case is dimension dimension 3, where we give an upper bound of 7 n^2 triangles, and a lower bound for some polygons P that require at least 1/2 n^2 triangles. In dimension 2 and dimensions 5 and above one needs only O(n) triangles. The case of dimension 4 is not completely resolved.
14 pages latex, 2 figures

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Geometric Topology, Differential Geometry, Metric Geometry, 53A10 (primary); 52B60, 57Q15 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/63370

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0202179
 http://arxiv.org/abs/math/0202179

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arXiv