Geodesic
On the Quasiisometric Mapping Preserving Simplex Orientation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 20-23 
A. V. Boluchevskaya. On the Quasiisometric Mapping Preserving Simplex Orientation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 20-23. http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper concerns simplex orientation preserving under the quasiisometric mapping. This problem arises from the problem of mesh generation using different kinds of mappings. We find the conditions for the quasiisometric mapping to be simplex orientation preserving.

[1] Azarenok B. N., On generation of dynamically adaptive spatial grids, Moscow, 2007, 50 pp. | MR | Zbl

[2] Miklukov V. M., Geometric analysis. Differential forms, almost-solutions, almost-quasiconformal mappings, Volgograd, 2007, 532 pp.

[3] Ushakova O. V., “Nondegeneracy conditions for three-dimensional cells and a formula for the cell's volume”, Comp. Math. and Math. Phys., 41:6 (2001), 832–845 | MR | Zbl

[4] Bobylev N. A., Kazunin A. V., Ivanenko S. A., “Piecewise smooth homeomorphisms of bounded domains and their applications to the theory of grids”, Comp. Math. and Math. Phys., 43:6 (2003), 772–781 | MR | Zbl

[5] Prohorova M. V., “Homeomorphism problems arising in the grid theory”, Trudy IMM UrO RAN, 14, no. 1, 2008, 112–129

[6] Klyachin V. A., “On homeomorphisms preserving triangulation”, Zapiski seminara «Sverhmedlennye processy», 4, 2009, 169–182

[7] Miklukov V. M., Introduction to non-smooth analysis, Volgograd, 2008, 424 pp.

[8] Kudryavcev L. D., Mathematical analysis, v. 2, Drofa, Moscow, 2004, 720 pp.

[9] Gantmacher F. R., The Theory of Matrices, AMS Chelsea Publishing; Amer. Math. Soc., 2000, 660 pp. | MR | MR