5 problems

Let $\Sigma^{2n-1}$ bound a strictly convex domain in $\mathbb{R}^{2n}$. Elliptic orbit conjecture. There exists at least one elliptic closed Reeb orbit on $\Sigma$. The source des…

Let $\Sigma^{2n-1}$ bound a convex domain in $\mathbb{R}^{2n}$, with $n\geq 2$, and let $\mathcal{T}(\Sigma)$ denote the set of prime closed Reeb orbits on $\Sigma$. A closed Reeb…

Let $\Sigma^{2n-1}$ bound a star-shaped domain in $\mathbb{R}^{2n}$. Higher-dimensional two-or-infinity conjecture. For each such $\Sigma$, … The dimension-four case is solved by t…

Let $\Sigma^{2n-1}$ be the boundary of a star-shaped domain in $\mathbb{R}^{2n}$, and let $\mathcal{T}(\Sigma)$ denote the set of prime closed Reeb orbits on $\Sigma$. Multiplicity…

Let $M$ be the smooth boundary of a star-shaped domain in ${\mathbb R}^{2n}$. A Reeb pseudo-rotation is a Reeb flow on $M$ with finitely many prime closed orbits. HZ-conjecture. Th…