6 problems

Let $\Sigma$ be a star-shaped hypersurface in $\mathbb{R}^{2n}$, equipped with the standard contact form, and call its closed Reeb orbits closed characteristics. A closed character…

Let $\Sigma$ be a star-shaped hypersurface in $\mathbb{R}^{2n}$, equipped with the standard contact form, and call its closed Reeb orbits closed characteristics. A closed character…

Let $n\geq 1$ and let $\Sigma\in{\cal H}_{st}(2n)$ be a compact strictly star-shaped hypersurface in ${\bf R}^{2n}$ enclosing the origin. Write $\,^{\#}{\cal T}(\Sigma)$ for the nu…

For an integer $n\geq2$, let ${\cal H}_{st}(2n)$ be the class of compact strictly star-shaped hypersurfaces in ${\bf R}^{2n}$, and let $\,^{\#}{\cal T}(\Sigma)$ denote the number o…

Star-shaped closed-characteristic count conjecture. The same lower bound should hold for every $\Sigma\in{\cal H}_{st}(2n)$:

Let $\Sigma$ be a compact star-shaped hypersurface in $\mathbb{R}^{2n}$, and suppose that it has only finitely many geometrically distinct closed characteristics. A closed characte…