Geodesic
Research in the field of geometric analysis at Volgograd state university
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 23 (2020) no. 2, pp. 5-21.

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

This article discusses the main directions of research in geometric analysis, which were conducted and are being carried out by the scientific mathematical school of Volgograd State University. The results of the founder of the scientific school, Doctor of Physics and Mathematics, Professor Vladimir Mikhailovich Miklyukov and his students are summarized. These results concern the solution of a number of problems in the field of quasiconformal flat mappings and mappings with bounded distortion of surfaces and Riemannian manifolds, the theory of minimal surfaces and surfaces of prescribed mean curvature, surfaces of zero mean curvature in Lorentz spaces, as well as problems associated with the study of the stability of such surfaces. In addition, the results of the study of various classes of triangulations — an object that appears at the junction of research in the field of geometric analysis and computational mathematics — are noted. Besides, this review discusses papers that use the Fourier decomposition method for solutions of the Laplace — Beltrami equations and the stationary Schrödinger equation with respect to the eigenfunctions of the corresponding boundary value problems. In particular, the authors give the results on finding capacitive characteristics that allowed for the first time to formulate and prove the criteria for the fulfillment of various theorems of Liouville type and the solvability of boundary value problems on model and quasimodel Riemannian manifolds. The role of the equivalent function method is also indicated in the study of such problems on manifolds of a fairly general form. \newpage In addition to this, the article gives an overview of the results concerning estimates of calculating error integral functionals and convergence of piecewise polynomial solutions of nonlinear variational type equations: minimal surface equations, equilibrium equations capillary surface and equations of biharmonic functions.
Keywords: geometric analysis, minimal surfaces, capacity, harmonic functions, integral functional.
Mots-clés : triangulation 
@article{VVGUM_2020_23_2_a0,
     author = {A. A. Klyachin and V. A. Klyachin},
     title = {Research in the field of geometric analysis at {Volgograd} state university},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {5--21},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2020_23_2_a0/}
}
TY  - JOUR
AU  - A. A. Klyachin
AU  - V. A. Klyachin
TI  - Research in the field of geometric analysis at Volgograd state university
JO  - Matematičeskaâ fizika i kompʹûternoe modelirovanie
PY  - 2020
SP  - 5
EP  - 21
VL  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VVGUM_2020_23_2_a0/
LA  - ru
ID  - VVGUM_2020_23_2_a0
ER  - 
%0 Journal Article
%A A. A. Klyachin
%A V. A. Klyachin
%T Research in the field of geometric analysis at Volgograd state university
%J Matematičeskaâ fizika i kompʹûternoe modelirovanie
%D 2020
%P 5-21
%V 23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VVGUM_2020_23_2_a0/
%G ru
%F VVGUM_2020_23_2_a0
A. A. Klyachin; V. A. Klyachin. Research in the field of geometric analysis at Volgograd state university. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 23 (2020) no. 2, pp. 5-21. http://geodesic.mathdoc.fr/item/VVGUM_2020_23_2_a0/