8 problems

Consider the three-dimensional wave equation associated with the inverse-square potential parameter $a$, with $-\frac{1}{4}<a<0$, and also the critical case $a=-\frac{1}{4}$. Let t…

Consider the inhomogeneous nonlinear Schrödinger equation with inverse-square potential in the focusing case, with parameters $N$, $\lambda$, and $b$, and let…

Let $g$ be an asymptotically flat metric and let $V$ be a non-singular, lower-order perturbation. Consider equations of the form … Here $\digamma$ is the inverse-square potential p…

Vortex instability conjecture. The orbital instability of two-dimensional vortex states is essentially due to the difference between Schrödinger flows with and without a repulsive…

Instability mechanism conjecture. The nature of the instability of central vortex states should be described by the effect of a repulsive inverse-square potential.

For $m$ with $4\operatorname{Re}m>-14$, let $H_m$ denote the family of closed operators defined by the preceding construction. A holomorphic family of closed operators is a paramet…

Consider the focusing energy-critical nonlinear Schrödinger equation in three dimensions with inverse-square potential, and let the threshold be the energy of its least-energy soli…

Let $k\in\mathbb{R}$ be arbitrary. Consider a quantum mechanical particle in $\mathbb{R}^3$ under the inverse square potential $k|x|^{-2}$, and let $\ell$ denote its orbital quantu…