Mathematics > Analysis of PDEs
arXiv:2606.16713 (math)
[Submitted on 15 Jun 2026]
Abstract:Under cone containment and the central ray hypothesis, we prove a determinant majorization result for hyperbolic polynomials on Euclidean Jordan algebras. In the case of real symmetric $n \times n$ matrices, this recovers the main theorem of Harvey and Lawson [Duke Math. J. 174 (2025), no. 13, 2749--2763] and also yields a new $\sigma_2$ majorization result. Moreover, for every $3 \leq k \leq n-1$, we construct explicit hyperbolic polynomials satisfying cone containment and the central ray hypothesis but for which the analogous $\sigma_k$ majorization fails.
Submission history
From: Doanh Pham [view email]
[v1]
Mon, 15 Jun 2026 13:40:59 UTC (16 KB)
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