Semialgebric rank-one convex hulls: 2x2 triangular matrices and beyond
Metric Geometry
2025-09-10 v1 Algebraic Geometry
Analysis of PDEs
Abstract
We prove that the rank-one convex hull of finitely many 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.
Cite
@article{arxiv.2509.07541,
title = {Semialgebric rank-one convex hulls: 2x2 triangular matrices and beyond},
author = {Chiara Meroni and Bogdan Raita},
journal= {arXiv preprint arXiv:2509.07541},
year = {2025}
}
Comments
18 pages, comments are welcome!