6 problems

Let $M$ be a smooth manifold with boundary, and let $g_1$ and $g_2$ be smooth metrics of Anosov type on $M$ such that … Assume that $g_1$ and $g_2$ have the same marked lens data,…

Burago–Ivanov conjecture. Every simple manifold is a strict minimal filling.

Michel's conjecture. All simple manifolds are boundary rigid.

Let $\Omega \subset \mathbb{C}^d$ be a bounded convex domain and let $\xi_0\in\partial\Omega$. A holomorphic self-map is a holomorphic map $f:\Omega\to\Omega$. The tangent cone of…

Let $\Omega \subset \mathbb{C}^d$ be a pseudoconvex domain of finite type and let $\xi_0 \in \partial \Omega$. A holomorphic self-map is a map $f:\Omega\to\Omega$ that is holomorph…

Let $M$ be a compact Riemannian manifold with boundary. It is a strict minimal filling if, for every compact Riemannian manifold $M'$ with $\partial M'=\partial M$, the inequalitie…