6 papers
Numerical exploration of the range of shape functionals using neural networks
Eloi Martinet, Ilias Ftouhi
We introduce a novel numerical framework for the exploration of Blaschke--Santaló diagrams, which are efficient tools characterizing the possible inequalities relating some given s…
Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue
Ilias Ftouhi
We prove that among all doubly connected domains of of the form , where and are open balls of fixed radii such that $\overl…
Complete systems of inequalities relating the perimeter, the area and the Cheeger constant of planar domains
Ilias Ftouhi
The object of the paper is to find complete systems of inequalities relating the perimeter , the area and the Cheeger constant of planar sets. To do so, we study t…
Improved description of Blaschke--Santaló diagrams via numerical shape optimization
Ilias Ftouhi
We propose a method based on the combination of theoretical results on Blaschke--Santaló diagrams and numerical shape optimization techniques to obtain improved description of Blas…
The monotonicity of the Cheeger constant for parallel bodies
Ilias Ftouhi
We prove that for every planar convex set , the function is monotonically decreasing, where , and stand for…
Sharp inequalities involving the Cheeger constant of planar convex sets
Ilias Ftouhi, Alba Lia Masiello, Gloria Paoli
We are interested in finding sharp bounds for the Cheeger constant via different geometrical quantities, namely the area , the perimeter , the inradius , the cir…