From G\aa rding's cones to $p$-convex hypersurfaces

N. M. Ivochkina

Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 94-104.

Résumé

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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