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Geometry of m-Hessian Equations

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Abstract

In the process of developing the modern theory of fully nonlinear, second-order partial differential equations, new geometric characteristics of surfaces naturally appeared. The implementation of these characteristics in terms of the classical differential geometry leads to significant technical difficulties. This paper provides a review of the necessary methodological reform and demonstrates a new differential geometric techniques by an example of constructing boundary barriers for m-Hessian equations.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    N. V. Filimonenkova

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  1. N. V. Filimonenkova
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Correspondence to N. V. Filimonenkova.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 169, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part II, 2019.

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Filimonenkova, N.V. Geometry of m-Hessian Equations. J Math Sci 263, 445–461 (2022). https://doi.org/10.1007/s10958-022-05941-6

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