Geometric properties of optimizers for the maximum gradient of the torsion function

par Phanuel Mariano (Union College)

lundi 19 oct. 2026, 16:00 → 17:00 Europe/Paris

313 (Site des Carmes)

The torsion function for a domain is a classical object in the theory of elasticity that

measures the resistance to twisting for a rod with cross-sections given by such domain.

Motivated by this, we consider an extremal problem for the maximum gradient of the

torsion function, ranging over bounded convex planar domains. We show that this

extremal problem admits a maximizer, and that any maximizer has a C^1 boundary

containing a line segment on which its gradient attains its maximum. The proofs are

probabilistic in nature and use novel coupling techniques. This talk is based on joint work

with Krzysztof Burdzy and Ilias Ftouhi.