23 citations · 41 across the 30 of their papers we have counts for
4 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…
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…