collaborators

5 papers

math.DS2026

Area-Normalized Pentagram Map Dynamics: Spectral Flattening and Elliptic Asymptotics

Michał Zwierzyński

The pentagram map sends a polygon to the intersections of consecutive short diagonals. We study its shape dynamics after translating and positively rescaling each iterate to restor…

math.DG2026

Mixed Volumes, the Wigner Caustic, and Isoperimetric Inequalities

Michał Zwierzyński

Let be a convex body and its central symmetral. We study the defects through the even--odd decomp…

math.DG2026

Convex Polygons with Parallel Opposite Sides: Convergence, Reconstruction, and Isoperimetric Inequalities

Izabella Konicer, Bartłomiej Murawski, Bruno Rogala +2

In this paper, we study affine -equidistants of convex polygons with parallel opposite sides (CPPOSes), introduced by M. Craizer et al. (Polygons with Parallel Opposite Sides,…

math.DG2026

The th Order Preserving Sets and Isoperimetric Type Inequalities for Planar Ovals

Maksymilian Filip Safarewicz, Michał Zwierzyński

In this work, we introduce and investigate a new class of sets, the \textit{th Order Preserving Sets}, arising naturally from the Fourier analysis of support functions associate…

math.DG2025

The Constant Width Measure Set, the Spherical Measure Set and isoperimetric equalities for planar ovals

M. Zwierzyński

In this paper we introduce the Constant Width Measure Set, which measures the constant width property of an oval, i.e. the planar simple closed strictly convex curve. We study its…