Ivochkina, N. M.; Prokof’eva, S. I.; Yakunina, G. V. On new functional characteristics of domains \(\Omega\in\mathbb{R}^n\). (English. Russian original) Zbl 1498.35319 Math. Notes 112, No. 1, 70-82 (2022); translation from Mat. Zametki 112, No. 1, 61-75 (2022). Summary: 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. MSC: 35J96 Monge-Ampère equations Keywords:Hesse matrix; domain mediators; Hessian dilation PDFBibTeX XMLCite \textit{N. M. Ivochkina} et al., Math. Notes 112, No. 1, 70--82 (2022; Zbl 1498.35319); translation from Mat. Zametki 112, No. 1, 61--75 (2022) Full Text: DOI References: [1] Ivochkina, N. M.; Prokof’eva, S. I.; Yakunina, G. V., Integral inequalities in the theory of Hessian operators, Math. Notes, 109, 4, 570-579 (2021) · Zbl 1468.35077 [2] Ivochkina, N. M., A description of the stability cones generated by differential operators of Monge-Ampère type, Sb. Math., 50, 1, 259-268 (1985) · Zbl 0556.35026 [3] Gårding, L., An inequality for hyperbolic polynomials, J. Math. Mech., 8, 957-965 (1959) · Zbl 0090.01603 [4] Ivochkina, N. M.; Filimonenkova, N. V., On two symmetries in the theory of \(m\)-Hesse operators, Topol. Methods Nonlinear Anal., 52, 1, 31-47 (2018) · Zbl 1447.58035 [5] Wang, X. J., A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J., 43, 25-54 (1994) · Zbl 0805.35036 [6] Ivochkina, N. M.; Filimonenkova, N. V., Differential Geometry in the Theory of Hessian Operators (2021) · Zbl 1481.35190 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.