Geodesic
A stochastic condition for minimal surfaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 54-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we obtain a stochastic criterion for a minimal surface in terms of transition densities of random processes generated by the fundamental forms of the surface.
Keywords: transition density of a random process, heat equation, mean curvature. 
@article{INTO_2020_181_a6,
     author = {D. S. Klimentov},
     title = {A stochastic condition for minimal surfaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {54--58},
     publisher = {mathdoc},
     volume = {181},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_181_a6/}
}
TY  - JOUR
AU  - D. S. Klimentov
TI  - A stochastic condition for minimal surfaces
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 54
EP  - 58
VL  - 181
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_181_a6/
LA  - ru
ID  - INTO_2020_181_a6
ER  - 
%0 Journal Article
%A D. S. Klimentov
%T A stochastic condition for minimal surfaces
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 54-58
%V 181
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_181_a6/
%G ru
%F INTO_2020_181_a6
D. S. Klimentov. A stochastic condition for minimal surfaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 54-58. http://geodesic.mathdoc.fr/item/INTO_2020_181_a6/

[1] Vatanabe S., Ikeda N., Stokhasticheskie differentsialnye uravneniya i diffuzionnye protsessy, Nauka, M., 1986

[2] Vekua I. N., Osnovy tenzornogo analiza i teorii kovariantov, Nauka, M., 1978 | MR

[3] Dynkin E. B., Markovskie protsessy, Fizmatlit, M., 1963

[4] Klimentov D. S., “Stokhasticheskii analog osnovnoi teoremy teorii poverkhnostei dlya poverkhnostei polozhitelnoi krivizny”, Izv. vuzov. Sev.-Kavkaz. region. Estestv. nauki., 2013, no. 6, 24–27

[5] Klimentov D. S., “Stokhasticheskii analog osnovnoi teoremy teorii poverkhnostei dlya poverkhnostei nenulevoi srednei krivizny”, Izv. vuzov. Sev.-Kavkaz. region. Estestv. nauki., 2014, no. 1, 15–18

[6] Finikov S. P., Kurs differentsialnoi geometrii, GITTL, M., 1952 | MR

[7] Fukushima M., Oshima Y., Takeda M., Dirishlet Forms and Symmetric Markov Processes, de Gruyter, Berlin–New York, 1994 | MR