Theory of bendings, partial differential equations, stochastic methods in differential geometry.
Main publications:
Klimentov S. B. Izgibaniya poverkhnostei roda $p\ge 0$ polozhitelnoi vneshnei krivizny. Ukr. geom. sb., v. 19, 1976, s. 37–56.
Fomenko V. T., Klimentov S. B., Ob izgibaniyakh poverkhnostei roda $p\ge q$ polozhitelnoi vneshnei krivizny v rimanovom prostranstve. DAN SSSR, t. 227, # 5, 1976, s. 1064–1066.
Fomenko V. T., Klimentov S. B. Neizgibaemost zamknutykh poverkhnostei roda $p\ge 1$ i polozhitelnoi vneshnei krivizny. Matem. sb., t. 101, # 3, 1976, s. 402–415.
Klimentov S. B. Globalnaya formulirovka osnovnoi teoremy teorii $n$-mernykh poverkhnostei v $m$-mernom prostranstve postoyannoi krivizny. Ukr. geom. sb., v. 22, 1979, s. 64–81.
Klimentov S. B. O deformatsiyakh zamknutykh poverkhnostei roda $p\ge 1$ s zadannym beskonechno malym izmeneniem metriki. Matem. sb., t. 108, # 3, 1979, s. 307–325.
Klimentov S. B. O strukture mnozhestva vsekh izometricheskikh preobrazovanii diffeomorfnoi krugu poverkhnosti polozhitelnoi krivizny. DAN SSSR, t. 262, # 1, 1982, s. 19–21.
Klimentov S. B. O strukture mnozhestva reshenii osnovnykh uravnenii teorii poverkhnostei. Ukr. geom. sb., v. 25, 1982, s. 69–82.
Klimentov S. B. O prodolzhenii beskonechno malykh izgibanii vysshikh poryadkov odnosvyaznoi poverkhnosti polozhitelnoi krivizny. Matem. zametki, t. 36, v. 3, 1984, s. 393–403.
Klimentov S. B. Ob odnom sposobe postroeniya reshenii kraevykh zadach teorii izgibanii poverkhnostei polozhitelnoi krivizny. Ukr. geom. sb., v. 29, 1986, s. 56–82.
Klimentov S. B. Ob izgibanii kuska ovaloida v poverkhnost s samoperesecheniem. Matem. zametki, t. 40, v. 1, 1986, s. 98–113.
Klimentov S. B. Ob apriornykh otsenkakh proizvodnykh radiusa-vektora poverkhnosti polozhitelnoi krivizny. Problemy geometrii, t. 19, Itogi nauki i tekhniki, 1987, s. 187–213.
Klimentov S. B. Nekotorye dostatochnye usloviya pogruzhaemosti v tselom metrik polozhitelnoi krivizny. Ukr. geom. sb., v. 34, 1991, s. 51–59.
Klimentov S. B. Stokhasticheskii analog formul Gaussa–Veingartena–Richchi dlya $n$-mernykh podmnogoobrazii $m$-mernogo prostranstva postoyannoi krivizny. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 1996, # 2, s. 17–20.
Klimentov S. B. Kvazikonformnye martingaly. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 1997, # 2, s. 21–23.
Goncharov A. L., Klimentov S. B. Ob izgibaniyakh poverkhnostei polozhitelnoi krivizny s izolirovannoi tochkoi uploscheniya. Izvestiya VUZov, Sev. -Kav. region, seriya "Estestvennye nauki", 1997, # 4, s. 13–21.
Klimentov S. B. Veroyatnostnoe predstavlenie resheniya kraevoi zadachi Rimana–Gilberta dlya golomorfnykh funktsii. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 2000, # 4, s. 7–9.
Klimentov S. B. Veroyatnostnoe predstavlenie resheniya kraevoi zadachi Rimana–Gilberta dlya uravneniya Beltrami. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 2000, # 4, s. 9–12.
Klimentov S. B. Veroyatnostnoe predstavlenie dlya beskonechno malykh izgibanii poverkhnostei polozhitelnoi krivizny. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 2001, # 4, s. 26–28.
Klimentov S. B. Klassy Khardi obobschennykh analiticheskikh funktsii. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 2003, # 3, s. 6–10.
Klimentov S. B. Stokhasticheskaya kraevaya zadacha Rimana–Gilberta v konformnykh martingalnykh klassakh. kompleksnomu analizu, teorii operatorov i matematicheskomu modelirovaniyu, Vladikavkaz, Izd-vo VNTs RAN, 2004, s. 75–89.
Klimentov S. B. Kraevaya zadacha Rimana–Gilberta v klassakh Khardi obobschennykh analiticheskikh funktsii. Izvestiya VUZov, Sev.-Kav. region, seriya "Estestvennye nauki", 2004, # 4, s. 3–5.
Goncharov A. L., Klimentov S. B. , Usmanov Z. D. Analog teoremy Liuvillya dlya odnogo klassa sistem tipa Koshi–Rimana s singulyarnymi koeffitsientami. Vladikavkazskii matematicheskii zhurnal, t. 7, v. 4, 2005, s. 7–16.
Klimentov S. B. Klassy BMO obobschennykh analiticheskikh funktsii. Vladikavkazskii matematicheskii zhurnal, t. 8, v. 1, 2006, s. 27–39.
S. B. Klimentov, “A priori estimates of the positive real or imaginary part of a generalized analytic function”, Vladikavkaz. Mat. Zh., 25:4 (2023), 50–57
2021
2.
S. B. Klimentov, “Second kind representations of Sobolev space solutions to a first order general elliptic linear system in a simply connected plane domain”, Sibirsk. Mat. Zh., 62:3 (2021), 538–554; Siberian Math. J., 62:3 (2021), 434–448
2019
3.
S. B. Klimentov, “On bending of surfaces of genus $p\geq 1$ of positive external curvature”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 169 (2019), 17–22
4.
S. B. Klimentov, “Unique determination of locally convex surfaces with boundary and positive curvature of genus $p\geqslant 0$”, Sibirsk. Mat. Zh., 60:1 (2019), 109–117; Siberian Math. J., 60:1 (2019), 82–88
S. B. Klimentov, “On isomorphism of some functional spaces under action of integro-differential operators”, Ufimsk. Mat. Zh., 11:1 (2019), 39–60; Ufa Math. J., 11:1 (2019), 42–62
S. B. Klimentov, “The Riemann–Hilbert problem in Hardy classes for general first-order elliptic systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 6, 36–47; Russian Math. (Iz. VUZ), 60:6 (2016), 29–39
S. B. Klimentov, “Some pathological examples of solutions to a Beltrami equation”, Sibirsk. Mat. Zh., 57:5 (2016), 1054–1061; Siberian Math. J., 57:5 (2016), 824–829
2014
9.
S. B. Klimentov, “Representations of the “second kind” for the hardy classes of solutions to the Beltrami equation”, Sibirsk. Mat. Zh., 55:2 (2014), 324–340; Siberian Math. J., 55:2 (2014), 262–275
S. B. Klimentov, “The Riemann–Hhilbert boundary value problem for generalized analytic functions in Smirnov classes”, Vladikavkaz. Mat. Zh., 14:3 (2012), 63–73
S. B. Klimentov, “Riemann–Hilbert boundary value problems in $BMO$ classes for generalized analytic functions”, Vladikavkaz. Mat. Zh., 13:1 (2011), 13–20
2010
12.
S. B. Klimentov, “Riemann and Hilbert boundary value problems in $BMO$ classes for holomorphic functions”, Vladikavkaz. Mat. Zh., 12:4 (2010), 28–38
A. L. Goncharov, S. B. Klimentov, Z. D. Usmanov, “An analogue of Liouville's theorem for a class of systems of Cauchy-Riemann type with singular coefficients”, Vladikavkaz. Mat. Zh., 7:4 (2005), 7–16
S. B. Klimentov, “A priori estimates for the derivatives of the radius-vector of a surface of positive curvature”, Itogi Nauki i Tekhniki. Ser. Probl. Geom., 19 (1987), 187–213; J. Soviet Math., 44:2 (1989), 215–235
S. B. Klimentov, “Bending of a piece of an ovaloid into a surface with self-intersection”, Mat. Zametki, 40:1 (1986), 98–114; Math. Notes, 40:1 (1986), 554–562
1984
17.
S. B. Klimentov, “Extensions of infinitesimal bendings of higher orders of a simply connected surface of positive curvature”, Mat. Zametki, 36:3 (1984), 393–403; Math. Notes, 36:3 (1984), 695–700
S. B. Klimentov, “On the structure of the set of all isometric transformations of a surface of positive curvature that is diffeomorphic to a disk”, Dokl. Akad. Nauk SSSR, 262:1 (1982), 19–21
1979
19.
S. B. Klimentov, “On deformations of closed surfaces of genus $p\geqslant1$ with given infinitesimal change of metric”, Mat. Sb. (N.S.), 108(150):3 (1979), 307–325; Math. USSR-Sb., 36:3 (1980), 283–299
V. T. Fomenko, S. B. Klimentov, “On bendings of surfaces of genus $p\ge0$ of positive extrinsic curvature in a Riemannian space”, Dokl. Akad. Nauk SSSR, 227:5 (1976), 1064–1066
S. B. Klimentov, “Deformability of surfaces of positive curvature”, Mat. Zametki, 19:5 (1976), 815–823; Math. Notes, 19:5 (1976), 478–483
22.
V. T. Fomenko, S. B. Klimentov, “Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature”, Mat. Sb. (N.S.), 101(143):3(11) (1976), 402–415; Math. USSR-Sb., 30:3 (1976), 361–372
A. V. Abanin, A. O. Vatulyan, M. I. Karyakin, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, V. A. Stukopin, “Sergej Nikolaevich Melikhov (on his 60's anniversary)”, Vladikavkaz. Mat. Zh., 22:2 (2020), 98–99
24.
A. O. Vatulyan, M. I. Karyakin, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, Yu. S. Nalbandjan, “Abanin Alexander Vasil'evich (on his 65's anniversary)”, Vladikavkaz. Mat. Zh., 22:1 (2020), 93–97
2019
25.
S. B. Klimentov, “On combinations of diffeomorphisms of curves and domains and some integral operators”, Vladikavkaz. Mat. Zh., 21:1 (2019), 79–84
2018
26.
A. V. Abanin, E. K. Basaeva, A. O. Vatulyan, S. K. Vodop'yanov, A. E. Gutman, V. A. Koibaev, Yu. F. Korobeinik, S. B. Klimentov, S. S. Kutateladze, A. A. Makhnev, B. B. Tasoev, S. M. Umarkhadzhiev, M. Z. Hudalov, “To the 65-th anniversary of prof. A. G. Kusraev”, Vladikavkaz. Mat. Zh., 20:2 (2018), 111–119
2017
27.
A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Alexey Borisovich Shabat (on his 80's anniversary)”, Vladikavkaz. Mat. Zh., 19:3 (2017), 83–85
2015
28.
A. O. Vatulyan, M. I. Karyakin, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, Yu. S. Nalbandjan, “Aleksandr Vasil'evich Abanin (on the occasion of his 60th anniversary)”, Vladikavkaz. Mat. Zh., 17:1 (2015), 78–81
2012
29.
A. O. Vatulyan, V. A. Kabel'kov, T. N. Kabel'kova, S. B. Klimentov, A. I. Kondratenko, A. G. Kusraev, A. N. Nikiforov, A. È. Pasenchuk, V. A. Rodin, V. G. Safronenko, S. M. Sitnik, A. N. Tkachev, V. G. Fetisov, “Aleksandr Nikolaevich Kabel'kov (1947–2011)”, Vladikavkaz. Mat. Zh., 14:2 (2012), 74–77
30.
A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Shabat Aleksei Borisovich (on his 75th birthday)”, Vladikavkaz. Mat. Zh., 14:2 (2012), 71–73
2010
31.
E. K. Basaeva, Yu. A. Kiryutenko, S. B. Klimentov, V. P. Kondakov, Yu. F. Korobeinik, A. G. Kusraev, M. A. Pliev, “Melikhov Sergei Nikolaevich (on his fiftieth birthday)”, Vladikavkaz. Mat. Zh., 12:2 (2010), 79–80
2004
32.
A. V. Abanin, M. M. Dragilev, A. I. Efimov, S. B. Klimentov, Yu. F. Korobeĭnik, A. G. Kusraev, V. F. Pulyaev, V. G. Fetisov, “Vladimir Petrovich Kondakov (on the occasion of his sixtieth birthday)”, Vladikavkaz. Mat. Zh., 6:2 (2004), 58–60
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