5 problems

Convex geodesic Swiss cheese conjecture. There exists such a finite disjoint union whose removal from $N$ delivers a metric $g_M$ of gradient type on $M$.

Let $M$ be a locally symmetric space of non-compact type with finite Riemannian volume. For $p\in M$, let $S_p(M)$ denote the unit tangent sphere at $p$, and let $E^+(p,\infty)$ be…

Let $M$ be a $d$-dimensional Riemannian manifold with or without boundary, where $d\geq 2$, and let $W_t(P)$ denote the wave front at time $t$ from a point $P\in M$. The wave front…

Let $G$ be a metabelian Carnot group, let $A\triangleleft G$ be an abelian subgroup with $[G,G]\subseteq A$, and let $V_1$ denote the first layer of $\operatorname{Lie}(G)$. Assume…

Let $(M,g)$ be a pinched negatively curved manifold. Let $(\mu_n)_n$ be a sequence of invariant probability measures converging vaguely to $\mu$, and let $F\in C_b(T^1M)$ be a unif…