5 papers · 1 filter
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…
The Geometry of the Centre Symmetry Set of a Planar Curve
Dominika Miller, MichaÅ ZwierzyÅski
The Centre Symmetry Set of a planar curve is the envelope of affine chords of , i.e. the lines joining points on with parallel tangent lines. In this paper we study glob…