6 problems

Triangle fail-point conjecture. The fail point lies on the longest side and is always closer to the foot of the altitude onto that side than to the midpoint of the side.

Ramaswamy's conjecture. The fail points occur either at the contact points of the largest inscribed circle or at points of minimal curvature.

Saint-Venant's conjecture. Fail points occur at the contact points of the largest inscribed circle.

Let $\Omega$ be an axially symmetric planar convex domain centered at the origin, and let the fail points be the points where the stress $|\nabla u|$ is maximal, with $u$ the torsi…

Let $\Omega$ be a convex planar domain symmetric about two coordinate axes, and call such a domain axially symmetric. The maximal stress is the maximum of $|\nabla u|$, where $u$ i…

Let $\Omega$ be a convex domain, and let the torsion function on $\Omega$ be the solution of the relevant Dirichlet problem. The largest inscribed circle of $\Omega$ intersects the…