9 problems

Let $(M^3,J,\theta)$ be a closed three-dimensional pseudohermitian manifold, and let $[\theta]$ denote its contact class. A contact form in this class is said to have vanishing CR…

Let $M$ be a strictly pseudoconvex CR manifold with contact form $\theta$, Tanaka–Webster connection $\nabla$, and associated metric $g_\theta$. Fix $x\in M$ and a $2$-plane…

Let $M$ be a Carnot–Carathéodory complete Sasakian manifold with pseudohermitian Ricci tensor $\rho$, and let $(\varphi,\xi,\eta,g)$ be its contact metric structure. For some…

Let $M$ be a strictly pseudoconvex CR manifold of dimension $2N-1$, let $\theta$ be a contact form, and let $S$ be a scalar pseudohermitian invariant satisfying the CR pluriharmoni…

Let $M^{2m+1}$ be a closed pseudohermitian manifold with vanishing pseudohermitian torsion $A_{\alpha\beta}=0$ and Webster Ricci tensor satisfying … Suppose a positive function $f$…

Let $(M^3,J,\theta,f,\mu)$ be a three-dimensional closed CR Yamabe soliton, where $P_0$ is the CR Paneitz operator. Assume that $P_0f=0$ and that $f$ is nowhere vanishing. Torsion…

Let $(M,\theta)$ be a closed pseudohermitian $(2n+1)$-manifold with $n\ge 2$. Assume that the Paneitz operator is nonnegative if $n=1$. Suppose there is a positive constant $k_0$ s…

Counterterm formula conjecture. The counterterm in the preceding topological-invariance conjecture is

Let the model be the generalized ellipsoid described in Section 2, equipped with the contact form $\vartheta$ defined in equation (polo). A CR map is said to preserve the Tanaka–We…