5 problems

Let $\gamma_t$, $t\in[0,1]$, be an eversion of a smooth circular wave front with no dangerous self tangencies: a family of generic oriented wave fronts in $\mathbb{R}^2$ whose endp…

Let a convex polygon billiard be a billiard in a convex polygonal table, and let $W_t(P)$ denote the billiard wave front at time $t$ from a point $P$ in the table. The wave front b…

Let a convex billiard table be a convex planar domain, and let $W_t(P)$ denote the billiard wave front at time $t$ from a point $P$ in the table. The wave front becomes dense if it…

Let $\mathbb{T}^d$ be the $d$-dimensional torus with $d>1$, equipped with a smooth Riemannian metric, and let $W_t(P)$ denote the wave front at time $t$ from a point…

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…