6 problems

Let $M$ be a manifold of dimension at least $2$. Let $(S^{\ast}M,\xi)$ be its spherical cotangent bundle with the standard contact structure, let $\alpha$ be a contact form with…

Let $(\xi^+,\xi^-)$ be a bicontact structure supporting an Anosov flow $X$. A Reeb flow is bitransverse when it has the bitransversality property required in the paper, and a flow…

Let $(xi^+,xi^-)$ be a bicontact structure supporting an Anosov flow $X$. The bicontact trichotomy conjecture. Exactly one of the following holds: 1. $xi^+$ is Anosov contact, it a…

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…

Reeb-flow entropy stability conjecture. The functional $h_{\rm top}$ is lower semi-continuous with respect to $d_{C^0}$.

Let $(M,\xi)$ be a contact 3-manifold. Let $X_\alpha$ be a Reeb vector field and $J$ a complex structure on the contact distribution, and let $\theta'$ denote the instantaneous rot…