Geodesic
Geometry of $m$-Hessian equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 98-115

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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.
Keywords: curvature matrix, $p$-curvature, $m$-Hessian equations, kernel of the boundary barrier.
Mots-clés : $m$-convex hypersurface 
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     author = {N. V. Filimonenkova},
     title = {Geometry of $m${-Hessian} equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {98--115},
     publisher = {mathdoc},
     volume = {169},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_169_a11/}
}
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N. V. Filimonenkova. Geometry of $m$-Hessian equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 98-115. http://geodesic.mathdoc.fr/item/INTO_2019_169_a11/