23 citations · 41 across the 30 of their papers we have counts for
6 papers · 1 filter
Mixed volumes and the Blaschke-Lebesgue theorem
Beniamin Bogosel
The mixed area of a Reuleaux polygon and its symmetric with respect to the origin is expressed in terms of the mixed area of two explicit polygons. This gives a geometric explanati…
Volume computation for Meissner polyhedra and applications
Beniamin Bogosel
The volume of a Meissner polyhedron is computed in terms of the lengths of its dual edges. This allows to reformulate the Meissner conjecture regarding constant width bodies with m…
A Geometric proof for the Polygonal Isoperimetric Inequality
Beniamin Bogosel
Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triang…
On the Blaschke-Lebesgue theorem for the Cheeger constant via areas and perimeters of inner parallel sets
Beniamin Bogosel
The first main result presented in the paper shows that the perimeters of inner parallel sets of planar shapes having a given constant width are minimal for the Reuleaux triangles.…
The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
Given a non-increasing and radially symmetric kernel in , we investigate counterparts of the classical Hardy-Littlewood and Riesz inequa…
On the numerical approximation of Blaschke-Santaló diagrams using Centroidal Voronoi Tessellations
Beniamin Bogosel, Giuseppe Buttazzo, Edouard Oudet
Identifying Blaschke-Santaló diagrams is an important topic that essentially consists in determining the image of a map , where the dimension of the…