23 citations · 41 across the 30 of their papers we have counts for
6 papers · 1 filter
New variational arguments regarding the Blaschke-Lebesgue theorem
Beniamin Bogosel
The sensitivity of the areas of Reuleaux polygons and disk polygons is computed with respect to vertex perturbations. Computations are completed for both constrained and Lagrangian…
A reverse isoperimetric inequality for convex shapes with inclusion constraint
Beniamin Bogosel
The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having…
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.…