Smooth hyperbolicity cones are second-order cone representable

Claus Scheiderer

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arXiv · 2509.17121

Smooth hyperbolicity cones are second-order cone representable

Claus Scheiderer

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Abstract

Netzer and Sanyal proved that every smooth hyperbolicity cone is a spectrahedral shadow. We generalize and sharpen this result at the same time, by showing that every Nash-smooth hyperbolicity cone is even second-order cone representable (socr). The result is proved as a consequence of our second theorem, according to which every compact convex semialgebraic set with Nash-smooth boundary of strict positive curvature is socr. The proof uses the technique of tensor evaluation.

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Claus Scheiderer. 2025-09-21. Smooth hyperbolicity cones are second-order cone representable. https://arxiv.org/abs/2509.17121

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