Semialgebric rank-one convex hulls: 2x2 triangular matrices and beyond
Abstract
We prove that the rank-one convex hull of finitely many 2× 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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