Semialgebric rank-one convex hulls: 2x2 triangular matrices and beyond
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909778768297984 |
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| author | Meroni, Chiara Raita, Bogdan |
| author_facet | Meroni, Chiara Raita, Bogdan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semialgebric rank-one convex hulls: 2x2 triangular matrices and beyond Meroni, Chiara Raita, Bogdan Metric Geometry Algebraic Geometry Analysis of PDEs 14P10 (Primary) 49J45, 26B25 (Secondary) 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. |
| title | Semialgebric rank-one convex hulls: 2x2 triangular matrices and beyond |
| topic | Metric Geometry Algebraic Geometry Analysis of PDEs 14P10 (Primary) 49J45, 26B25 (Secondary) |
| url | https://arxiv.org/abs/2509.07541 |