Shurkaeva D.V. The estimate of the distortion of the tetrahedron isoperimetricity coefficient under bi-lipschitz mapping

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Shurkaеva Diana Vasil’еvna

Assistant Teacher, Department of Computer Science and Experimental Mathematics Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. The article assesses the tetrahedron isoperimetricity coefficient obtained by quasi-isometric mapping through the original tetrahedron isoperimetricity coefficient. This coefficient determines the condition of finiteness conservation of gradient for tetrahedral mesh under quasi-isometric mapping.

     Main Results: Let’s in the space given tetrahedron T, in which the length of the maximum edge is equal to d, the minimum is a, the lower face area is S, and  is bi-Lipschitz mapping with constants  then isoperimetricity coefficient of the tetrahedron image estimates as

Key words: coefficient of isoperimetricity, tetrahedron, Cayley — Menger determinant, Heron — Tartaglia formula, bi-Lipschitz mapping, quasi-isometric mapping.

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The estimate of the distortion of the tetrahedron isoperimetricity coefficient under bi-lipschitz mapping by Shurkaeva D.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (19) 2013 pp. 67-70

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