4 problems

Let the geometric $\alpha$-stable process be the symmetric Lévy process with characteristic exponent $\Psi(\xi)=\log(1+|\xi|^\alpha)$, and let $d$ denote the spatial dimension. The…

Let a quadratic center have a period annulus with an outer boundary, and define its criticality at the outer boundary as the maximal number of critical periodic orbits produced the…

Let $\Omega\subset\mathbb{R}^3$ be a smooth bounded domain, let $a$ be critical in $\Omega$, and let $G_a$ be the Dirichlet Green's function of $-\Delta+a$ normalized by … with reg…

Let $M$ be a Riemannian manifold, and let $P_+$ and $P_0$ be respectively subcritical and critical operators in $M$. Critical-subcritical decay conjecture. The ratio … locally unif…