5 papers
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…
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…
Convex Polygons with Parallel Opposite Sides: Convergence, Reconstruction, and Isoperimetric Inequalities
Izabella Konicer, BartÅomiej 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,…
The th Order Preserving Sets and Isoperimetric Type Inequalities for Planar Ovals
Maksymilian Filip Safarewicz, MichaÅ ZwierzyÅski
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…
The Constant Width Measure Set, the Spherical Measure Set and isoperimetric equalities for planar ovals
M. ZwierzyÅski
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…