8 papers
Polygonal Faber-Krahn inequality: Local minimality via validated computing
Beniamin Bogosel, Dorin Bucur
The main result of the paper shows that the regular -gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among -gons having fixed area for . Th…
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…
Optimization of Neumann Eigenvalues under convexity and geometric constraints
Beniamin Bogosel, Antoine Henrot, Marco Michetti
In this paper we study optimization problems for Neumann eigenvalues among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, tho…
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.…