3 problems

Distance equality conjecture. The distances $d_T$ and $d_F$ coincide on these isometry classes. The inequality $d_T\leq d_F$ is established, and equality is known on Teichmüller sp…

Hypoelliptic damping conjecture. The second part of the theorem for the elliptically perturbed operator $P_\epsilon$ holds with $\widetilde P_\epsilon$ in place of $P_\epsilon$. Th…

Let $M$ be a 3-manifold and let $f:M\to M$ be a partially hyperbolic diffeomorphism with invariant bundles $E^u$, $E^c$, and $E^s$. An embedded torus is periodic if $f^k(S)=S$ for…