3 problems

Let $(\Omega,d_\Omega)$ and $(\Omega',d_{\Omega'})$ be Hilbert geometries, where $\Omega$ and $\Omega'$ are convex domains equipped with their Hilbert metrics. They are projectivel…

Let $\Omega$ be an open bounded convex domain, and let a cone over $\Omega$ mean an open proper convex cone whose projectivization contains $\Omega$. A non-projective isometry is a…

Let $\Omega$ be an open bounded convex domain in an affine subspace of $\mathbb{RP}^n$. Write $Isom(\Omega)$ for its Hilbert-metric isometry group. de la Harpe's conjecture. The gr…