On New Functional Characteristics of Domains $\Omega\in\mathbb R^n$
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 61-75.

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A system of new differential-geometric notions as the result of an analysis of the Trudinger–Wang inequalities is proposed. Their naturalness in multivariate analysis and geometry is exhibited by an example of a model problem for the ball. New directions in the development of the theory of Hessian operators and their connection with geometry are noted.
Mots-clés : Hesse matrix, Hessian dilation.
Keywords: domain mediators
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N. M. Ivochkina; S. I. Prokof'eva; G. V. Yakunina. On New Functional Characteristics of Domains $\Omega\in\mathbb R^n$. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 61-75. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a5/

[1] N. M Ivochkina, S. I. Prokofeva, G. V. Yakunina, “Integralnye neravenstva v teorii gessianovskikh operatorov”, Matem. zametki, 109:4 (2021), 552–563 | DOI | MR | Zbl

[2] N. M. Ivochkina, “Opisanie konusov ustoichivosti, porozhdaemykh differentsialnymi operatorami tipa Monzha–Ampera”, Matem. sb., 122 (164):2 (10) (1983), 265–275 | MR | Zbl

[3] L. Gårding, “An inequality for hyperbolic polynomials”, J. Math. Mech., 8 (1959), 957–965 | MR

[4] N. M. Ivochkina, N. V. Filimonenkova, “On two symmetries in the theory of $m$-Hessian operators”, Topol. Methods Nonlinear Anal., 52:1 (2018), 31–47 | MR | Zbl

[5] X. J. Wang, “A class of fully nonlinear elliptic equations and related functionals”, Indiana Univ. Math. J., 43 (1994), 25–54 | DOI | MR | Zbl

[6] N. M. Ivochkina, N. V. Filimonenkova, Differential Geometry in the Theory of Hessian Operators, 2021, arXiv: 1904.04157v2