3 problems

Let $M$ be a compact manifold, let $H\in C^2(T^*M)$ be a Tonelli Hamiltonian, and let $u$ be a weak KAM solution of … where $c$ is Mañé's critical value. Write $\mathrm{Cut}(u)$ fo…

Let $v^T(x,s):=u^T(x,sT)$ and $u^T(s):=m^T(sT)$ for $sin[0,1]$ and $xinmathbb{R}^n$, and let $c$ be the critical value in the ergodic problem. Write the first equation of that pro…

Common critical subsolution conjecture. If $[H_1,H_2]=0$, then there exists at least one common $C^{1,1}$ subsolution for