The estimate of the distortion of the tetrahedron isoperimetricity coefficient under bi-Lipschitz mapping

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 : R3 → R3 is bi-Lipschitz mapping with constants