6 papers · 1 filter
Singularities of the Wigner Caustic and the Centre Symmetry Set of Frontal Curves in the Euclidean Plane
Michał Zwierzyński
Motivated by the role of the Wigner caustic in semiclassical phase-space analysis, we extend it, together with the centre symmetry set, from regular planar curves to cooriented fro…
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, 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, D…
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…
Singular points of the Wigner caustic and affine equidistants of planar curves
W. Domitrz, M. Zwierzyński
In this paper we study singular points of the Wigner caustic and affine --equidistants of planar curves based on shapes of these curves. We generalize the Blaschke-Süss theorem…
The Gauss-Bonnet Theorem for coherent tangent bundles over surfaces with boundary and its applications
Wojciech Domitrz, Michał Zwierzyński
In [31,32,33] the Gauss-Bonnet formulas for coherent tangent bundles over compact oriented surfaces (without boundary) were proved. We establish the Gauss-Bonnet theorem for cohere…