Semialgebraic rank-one convex hulls: 2x2 triangular matrices and beyond

Chiara Meroni; Bogdan Raita

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arXiv · 2509.07541

Semialgebraic rank-one convex hulls: 2x2 triangular matrices and beyond

Chiara Meroni·Bogdan Raita

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Abstract

We prove that the rank-one convex hull of finitely many $2\times 2$ triangular matrices is a semialgebraic set, defined by linear and quadratic polynomials. We present explicit constructions for five-point configurations and offer evidence suggesting that a similar characterization does not hold in the more general setting of directional convexity.

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Chiara Meroni, Bogdan Raita. 2025-09-09. Semialgebraic rank-one convex hulls: 2x2 triangular matrices and beyond. https://arxiv.org/abs/2509.07541

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