Minimum-area axially symmetric convex bodies containing a triangle and its measure of axial symmetry.
Minkowskian rhombi and squares inscribed in convex Jordan curves
We show that any convex Jordan curve in a normed plane admits an inscribed Minkowskian square. In addition we prove that no two different Minkowskian rhombi with the same direction of one diagonal can be inscribed in the same strictly convex Jordan curve.
Misure approssimanti ed insiemi ad ampiezza costante
Monotonic rearrangements of functions with small mean oscillation
We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous" ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named α-extension.
Nearly regular cell-decompositions of orientable 2-manifolds with at most two exceptional cells
Nonexistence of Curvature in Most Points of Most Convex Surfaces.
On a characterization of circles and spheres.
On a covering problem in the plane.
On a measure of axiality for triangular domains.
On a special family of compact convex sets in the Euclidean plane .
On area and side lengths of triangles in normed planes
Let be a d-dimensional normed space with norm ||·|| and let B be the unit ball in . Let us fix a Lebesgue measure in with . This measure will play the role of the volume in . We consider an arbitrary simplex T in with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of are determined. For d ≥ 3 it is noticed that the tight lower bound of is zero.
On Barbier's theorem
On boundary arcs joining antipodal points of a planar convex body.
On coverings of plane convex sets by translates of strips.
On Gnomons
On local and global moduli of convexity
On maximal ot-subsets of the Euclidean plane.
On minimum area quadrilaterals and triangles circumscribed about convex plane regions.
On minimum kissing numbers of finite translative packings of a convex body.
On parametric density of finite circle packings.