Research extrinsic geometric properties of extremal surfaces for various types of functionals (minimal surfaces, surfaces of constant mean curvature).
Computer graphics, mathematical methods of computer graphics, image analysis, computer graphics algorithms, grid generation methods of analysis and geometry, computational geometry.
Main publications:
Klyachin V. A. Otsenka protyazhennosti trubchatykh minimalnykh
poverkhnostei proizvolnoi korazmernosti. Sib. mat. zh. T. 33. 1992. N. 5. S.~201–206.
Klyachin V. A. Maksimalnye trubchatye poverkhnosti proizvolnoi
korazmernosti v prostranstve Minkovskogo. Izv. RAN. Ser. matem. T. 57. 1993. N. 4. S. 118–131.
Klyachin V. A. Novye primery trubchatykh minimalnykh poverkhnostei
proizvolnoi korazmernosti. Mat. zametki. T. 62. 1997. N. 1. S. 154–156.
Klyachin V. A. Issledovanie reshenii uravneniya poverkhnostei nulevoi srednei krivizny v prostranstve Minkovskogo. DAN Rossii. T. 384. 2002. N. 5. S. 587–589.
Klyachin V. A. Ob asimptoticheskikh svoistvakh maksimalnykh trubok i lent v okrestnosti izolirovannoi osobennosti v prostranstve Minkovskogo. Sib. mat. zh. T. 43. 2002. N. 1. S. 76–89.
Klyachin V. A. Poverkhnosti nulevoi srednei krivizny smeshannogo tipa
v prostranstve Minkovskogo. Izv. RAN. Ser. mat. T. 67. 2002. N. 2. S. 7–20.
Klyachin V. A., Miklyukov V. M. Maksimalnye giperpoverkhnosti
trubchatogo tipa v prostranstve Minkovskogo. Izv. AN SSSR. Ser. mat. N. 55. 1991. N. 1. S. 206–217.
Klyachin V. A., Miklyukov V. M. Ob odnom emkostnom priznake neustoichivosti minimalnykh giperpoverkhnostei.
DAN Rossii. T. 330. 1993. N. 4. S. 424–426.
Klyachin V. A., Miklyukov V. M. Usloviya konechnosti vremeni suschestvovaniya maksimalnykh trubok i lent v iskrivlennykh lorentsevykh
proizvedeniyakh. Izv. RAN. Ser. mat. T. 58. 1994. N. 3. S. 196–210.
Klyachin V. A., Miklyukov V. M. Priznaki neustoichivosti poverkhnostei
nulevoi srednei krivizny v iskrivlennykh lorentsevykh proizvedeniyakh. Matem. sb. T.~187. 1996. N. 11. S. 67–88.
Klachin V. A., Miklyukov V. M. Geometrical structure of tubes and bands of zero mean curvature in Minkowski space. Annales Academiae Scientiarum Fennicae, Mathematica. V. 28. 2003. P. 239–270.
Klyachin V. A. O nekotorykh svoistvakh ustoichivykh i neustoichivykh poverkhnostei predpisannoi srednei krivizny. Izv. RAN. Ser. matem., T. 70. 2006. S. 77–90.
Vladimir A. Klyachin, Vladislav V. Kuzmin, “On the existence of approximate solutions of variational problems in nonlinear elasticity theory”, Bulletin of Irkutsk State University. Series Mathematics, 53 (2025), 51–68
2.
V. A. Klyachin, “On mappings with bounded distortion of triangles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2025, no. 9, 50–57
2024
3.
V. A. Klyachin, “Estimates for piecewise linear approximation of derivative functions of Sobolev classes”, Bulletin of Irkutsk State University. Series Mathematics, 49 (2024), 78–89
Vladimir A. Klyachin, Vladislav V. Kuzmin, Ekaterina V. Khizhnyakova, “Triangulation method for approximate solving of variational problems in nonlinear elasticity”, Bulletin of Irkutsk State University. Series Mathematics, 45 (2023), 54–72
A. A. Klyachin, V. A. Klyachin, “Uniqueness theorems for recovering the inverse image under degenerate transformations”, Izv. Saratov Univ. Math. Mech. Inform., 22:1 (2022), 15–27
6.
V. A. Klyachin, E. G. Grigorieva, “Uniqueness theorem of reconstruction of preimage by its image under degenerate mapping”, Mathematical Physics and Computer Simulation, 25:2 (2022), 17–22
V. A. Klyachin, N. A. Chеbanеnko, “On geometrical properties of continuous mappings which preserve orientation of simplices”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 985–996
8.
A. A. Klyachin, V. A. Klyachin, “Algorithm for restoring the surface of an object from its image”, Mathematical Physics and Computer Simulation, 24:1 (2021), 16–24
A. A. Klyachin, V. A. Klyachin, “Existence and uniqueness theorems for solutions of inverse problems of projective geometry for 3D reconstruction from photographs”, Chebyshevskii Sb., 21:4 (2020), 117–128
10.
E. G. Grigorieva, V. A. Klyachin, “The study of the statistical characteristics of the text based on the graph model of the linguistic corpus”, Izv. Saratov Univ. Math. Mech. Inform., 20:1 (2020), 116–126
V. A. Klyachin, E. G. Grigorieva, “A 3D reconstruction algorithm of a surface of revolution from its projection”, Sib. Zh. Ind. Mat., 23:1 (2020), 84–92; J. Appl. Industr. Math., 14:1 (2020), 85–91
A. A. Klyachin, V. A. Klyachin, “Research in the field of geometric analysis at Volgograd state university”, Mathematical Physics and Computer Simulation, 23:2 (2020), 5–21
2019
13.
A. A. Klyachin, V. A. Klyachin, “The approximation of the fourth-order partial differential equations in the class of the piecewise polynomial functions on the triangular grid”, Mathematical Physics and Computer Simulation, 22:2 (2019), 65–72
V. A. Klyachin, “Approximation of the gradient of a function on the basis of a special
class of triangulations”, Izv. RAN. Ser. Mat., 82:6 (2018), 65–77; Izv. Math., 82:6 (2018), 1136–1147
V. A. Klyachin, E. G. Grigorieva, “Description of functionals that are minimized by $\Phi$-triangulations”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139 (2017), 9–14; Journal of Mathematical Sciences, 241:3 (2019), 251–257
16.
V. A. Klyachin, N. A. Chеbanеnko, “On the geometric structure of the continuos mappings preserving the orientation of simplexes”, Izv. Saratov Univ. Math. Mech. Inform., 17:3 (2017), 294–303
V. A. Klyachin, “On continuity and differentiability of the maximum values of functions”, Ufimsk. Mat. Zh., 9:4 (2017), 55–59; Ufa Math. J., 9:4 (2017), 54–58
18.
A. V. Boluchevskaya, V. A. Klyachin, M. E. Sapraliev, “Estimations of clearance radius for finite subset of a unit ball in ${\mathbb{R}}^{n}$”, Mathematical Physics and Computer Simulation, 20:3 (2017), 6–17
19.
E. G. Grigor'eva, V. A. Klyachin, A. A. Klyachin, “Universal software for solving multidimensional variational problems”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2017, no. 2(39), 39–55
V. A. Klyachin, M. I. Kazanin, “Construction of the solutions of the Monge–Ampere type equation based on $\Phi$-triangulation”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2017, no. 1(38), 6–12
2016
21.
V. A. Klyachin, “Modified Delaunay empty sphere condition in the problem of approximation of the gradient”, Izv. RAN. Ser. Mat., 80:3 (2016), 95–102; Izv. Math., 80:3 (2016), 549–556
V. A. Klyachin, “On the solvability of the discrete analogue of the Minkowski–Alexandrov problem”, Izv. Saratov Univ. Math. Mech. Inform., 16:3 (2016), 281–288
23.
E. G. Grigorieva, V. A. Klyachin, “Mathematical model of 3D maps and design of information system for its control”, J. Comp. Eng. Math., 3:4 (2016), 51–58
V. A. Klyachin, D. V. Shurkaeva, “Isoperimetry coefficient for simplex in the problem of approximation of derivatives”, Izv. Saratov Univ. Math. Mech. Inform., 15:2 (2015), 151–160
V. A. Klyachin, “Parallel algorithm of geometrical hashing based on NumPy package and processes pool”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2015, no. 4(29), 13–23
27.
V. A. Klyachin, “Triangulation algorithm based on empty convex set condition”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2015, no. 3(28), 27–33
V. A. Klyachin, E. G. Grigoreva, “Numerical study of the stability of equilibrium surfaces using NumPy package”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2015, no. 2(27), 17–30
V. A. Klyachin, “Optimization of Calculus Mesh for Cryobiology Problem Based on Multidimensional Hashing Using NumPy”, Izv. Saratov Univ. Math. Mech. Inform., 14:3 (2014), 355–362
V. A. Klyachin, N. A. Chеbanеnko, “About linear preimages of continuous maps, that preserve orientation of triangles”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2014, no. 3(22), 56–60
V. A. Klyachin, “Application of the method of sorting Schwartzian transform in the computational geometry”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1. Mathematica. Physica, 2014, no. 1(20), 14–21
2012
32.
V. A. Klyachin, “On a multidimensional analogue of the Schwarz example”, Izv. RAN. Ser. Mat., 76:4 (2012), 41–48; Izv. Math., 76:4 (2012), 681–687
V. A. Klyachin, A. A. Shirokii, “The Delaunay triangulation for multidimensional surfaces and its approximative properties”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 31–39; Russian Math. (Iz. VUZ), 56:1 (2012), 27–34
V. A. Klyachin, E. A. Pabat, “The $C^1$-approximation of the level surfaces of functions defined on irregular meshes”, Sib. Zh. Ind. Mat., 13:2 (2010), 69–78
V. A. Klyachin, A. A. Shiroky, “Delaunay triangulation of multidimensional surfaces”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2010, no. 4(78), 51–55
V. A. Klyachin, N. M. Medvedeva, “On the stability of extremal surfaces for a certain area type functional”, Sib. Èlektron. Mat. Izv., 4 (2007), 113–132
V. A. Klyachin, “On some properties of stable and unstable surfaces with prescribed mean curvature”, Izv. RAN. Ser. Mat., 70:4 (2006), 77–90; Izv. Math., 70:4 (2006), 717–730
V. A. Klyachin, “Zero mean curvature surfaces of mixed type in Minkowski space”, Izv. RAN. Ser. Mat., 67:2 (2003), 5–20; Izv. Math., 67:2 (2003), 209–224
V. A. Klyachin, “On asymptotic properties of maximal tubes and bands in a neighborhood of an isolated singularity in Minkowski space”, Sibirsk. Mat. Zh., 43:1 (2002), 76–89; Siberian Math. J., 43:1 (2002), 56–67
V. A. Klyachin, V. M. Miklyukov, “Criteria of instability of surfaces of zero mean curvature in warped Lorentz products”, Mat. Sb., 187:11 (1996), 67–88; Sb. Math., 187:11 (1996), 1643–1663
V. A. Klyachin, V. M. Miklyukov, “Conditions for finite existence time of maximal tubes and bands in Lorentzian warped products”, Izv. RAN. Ser. Mat., 58:3 (1994), 196–210; Russian Acad. Sci. Izv. Math., 44:3 (1995), 629–643
V. A. Klyachin, V. M. Miklyukov, “A capacity condition for the instability of minimal hypersurfaces”, Dokl. Akad. Nauk, 330:4 (1993), 424–426; Dokl. Math., 47:3 (1993), 509–512
V. A. Klyachin, “Estimation of the expansion of tubular minimal surfaces of arbitrary codimension”, Sibirsk. Mat. Zh., 33:5 (1992), 201–205; Siberian Math. J., 33:5 (1992), 928–932
V. A. Klyachin, V. M. Miklyukov, “Maximal tubular hypersurfaces in Minkowski space”, Izv. Akad. Nauk SSSR Ser. Mat., 55:1 (1991), 206–217; Math. USSR-Izv., 38:1 (1992), 203–213
F. G. Avkhadiev, V. A. Botvinnik, S. K. Vodop'yanov, M. Vuorinen, V. M. Gol'dstein, V. V. Goryainov, A. A. Grigor'yan, V. N. Dubinin, I. V. Zhuravlev, V. A. Zorich, V. M. Kesel'man, A. A. Klyachin, V. A. Klyachin, T. G. Latfullin, A. V. Loboda, A. G. Losev, O. Martio, V. I. Pelikh, S. I. Pinchuk, Yu. G. Reshetnyak, A. S. Romanov, A. G. Sergeev, V. G. Tkachev, E. M. Chirka, “Vladimir Mikhailovich Miklyukov (obituary)”, Uspekhi Mat. Nauk, 69:3(417) (2014), 173–176; Russian Math. Surveys, 69:3 (2014), 565–568
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