6 problems

Uniform a priori estimate conjecture. There exists $C(M,g,\delta)>0$ such that

Donald's conjecture. For any $k\geqslant 0$, one can bound $\|\tilde{\omega}\|_{C^k(M,g)}$ by a constant depending only on $k$ and on bounds for $\sigma$, $\omega$, and $(M,J)$, wh…

Let $(M,\omega)$ be a compact symplectic manifold of real dimension $4$, equipped with an almost complex structure $J$ tamed by $\omega$. Let $\tilde{\omega}$ be another symplectic…

Let $(u,p,u_0,0,T,L)$ be a smooth periodic, homogeneous normalised-pressure solution, with $0<T<T_0<\infty$ and periodic data norm ${\mathcal H}^1(u_0,0,T,L)\leq A<\infty$. A prior…

Let $(u,p,u_0,0,T)$ be a smooth homogeneous $H^1$ solution, with $\|u_0\|_{H^1_x(\mathbf{R}^3)}\leq A<\infty$. A priori global homogeneous $H^1$ bound. There exists a function…

Let $(u,p,u_0,f,T,L)$ be a smooth periodic, normalised-pressure solution, with periodic $H^1$ data norm ${\mathcal H}^1(u_0,f,T,L)$ finite. A priori periodic $H^1$ bound. There exi…