Martin Winter

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20242026

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math.CO2026

A relation between Mahler volume and flag number for convex polytopes

Martin Winter

Given a convex polytope $P \subset R^{d}$ with $F (P)$ many flags, we prove $vol (P) vol (P - P)^{\circ} \leq \frac{F ( P )}{( d ! ) ^{2}} .$ This…

math.MG2026

A short polyhedral proof of the infinitesimal Stoker conjecture

Martin Winter

The infinitesimal Stoker conjecture states that an infinitesimal deformation of a convex polytope that preserves all dihedral angles also preserves all normal directions up to isom…

math.CO2026

Deformations and second-order rigidity of polytopes

Matthias Adrian-Himmelmann, Martin Winter, Zhen Zhang

We study deformations of polytopes that preserve edge lengths and face coplanarities. This gives rise to a notion of rigidity, for which we develop a second-order theory together w…