Ilias Ftouhi

collaborators

5 papers

math.OC2026

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--SantalÃ³ diagrams, which are efficient tools characterizing the possible inequalities relating some given…

math.OC2025

The monotonicity of the Cheeger constant for parallel bodies

Ilias Ftouhi

We prove that for every planar convex set $I^c ◯$ , the function $t \in (- r (I^c ◯), + \infty) ⟼ ∣ I^c ◯_{t} ∣ h (I^c ◯_{t})$ is monotonically decreasing, where $r$ , $∣ \cdot ∣$ and $h$ stand…

math.OC2025

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 $R^{n}$ of the form $B_{1} \ B_{2}$ , where $B_{1}$ and $B_{2}$ are open balls of fixed radii such that $\overl…

math.OC2025

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 $P$ , the area $∣ \cdot ∣$ and the Cheeger constant $h$ of planar sets. To do so, we study t…

math.OC2025

Improved description of Blaschke--SantalÃ³ diagrams via numerical shape optimization

Ilias Ftouhi

We propose a method based on the combination of theoretical results on Blaschke--SantalÃ³ diagrams and numerical shape optimization techniques to obtain improved description of Bla…