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From Gårding’s Cones to p-Convex Hypersurfaces

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Abstract

We consider cones discovered by Gårding in 1959. They play the fundamental role in the modern theory of fully nonlinear second-order partial differential equations. A new classification of symmetric matrices is presented based on the m-positiveness property. Such a classification establishes a new trend in geometry, generating a notion of m-convex hypersurfaces.

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Authors and Affiliations

  1. St.-Petersburg State University of Architecture and Civil Engineering 4, 2nd Krasnoarmeiskaya st., 198005, St.-Petersburg, Russia

    N. M. Ivochkina

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  1. N. M. Ivochkina
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Correspondence to N. M. Ivochkina.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 45, Proceedings of the Sixth International Conference on Differential and Functional Differential Equations and International Workshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 14–21 August, 2011). Part 1, 2012.

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Ivochkina, N.M. From Gårding’s Cones to p-Convex Hypersurfaces. J Math Sci 201, 634–644 (2014). https://doi.org/10.1007/s10958-014-2016-7

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  • DOI: https://doi.org/10.1007/s10958-014-2016-7

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