$${\mathcal {K}}$$-Lorentzian Polynomials
Abstract
Abstract Lorentzian polynomials are a fascinating class of real polynomials with many applications. Their definition is specific to the nonnegative orthant. Following recent work, we examine Lorentzian polynomials on proper convex cones. For a self-dual cone $${\mathcal {K}}$$ K we find a connection between $${\mathcal {K}}$$ K -Lorentzian polynomials and $${\mathcal {K}}$$ K -positive linear maps, which were studied in the context of the generalized Perron-Frobenius theorem. We find that as the cone $${\mathcal {K}}$$ K varies, even the set of quadratic $${\mathcal {K}}$$ K -Lorentzian polynomials can be difficult to understand algorithmically. We also show that, just as in the case of the nonnegative orthant, $${\mathcal {K}}$$ K -Lorentzian and $${\mathcal {K}}$$ K -completely log-concave polynomials coincide.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Black Holes and Theoretical Physics
Publication details
- Journal / source
- Discrete & Computational Geometry
- Publisher
- Springer Science and Business Media LLC
- Volume
- 76
- Issue
- 3
- Pages
- 1725-1741
- Publication date
- 13 April 2026
- Language
- EN