6 problems

Capacity conjecture. The existence of minimizers of $E_\kappa$ in $\mathcal{J}$ is completely determined by the value of $\operatorname{cap}(A)$ and the value of $\kappa$.

Let $(\psi\equiv 0,a=a^{b_r})$ be the constant-curvature solution (1.3), let $(\psi,a)$ be the solution (1.7), and let $h_r$ be the relevant Hermitian metric. Let $b_r$ and…

Let $(\psi,a)$ be the solution in (1.7) constructed under the assumptions of Theorem 1.1, let $h_r$ be the relevant Hermitian metric, and let $b_r$ and $\kappa$ be the parameters a…

Let $u_\varepsilon$ be a solution of the Ginzburg–Landau system in a smooth domain, and let $N_\varepsilon$ denote the boundary-energy quantity appearing in the regime of Theorem 1…

The energy functional $E$ admits global minimizers with localized vortices, and let their rescaled local profile be the profile near such a vortex. Generalized second Painlevé prof…

Consider a stochastically forced version of the full Gor'kov–Eliashberg equations … For each $\varepsilon>0$, let the forcing be strong enough that the resulting system admits an i…