16 problems

Let $(\Omega,\varrho)$ be a domain with the boundary conditions and elliptic problem specified by … admits at most one positive bounded solution. The paper's methods do not treat c…

Uniqueness conjecture. If $\alpha=4\pi$ and $\Omega$ is a ball, then the maximizers of the Trudinger–Moser inequality are unique.

Uniqueness conjecture. If

Let $G$ be a countably infinite graph of maximum degree … , the hard-core lattice gas on $G$ has a unique Gibbs measure whenever … for all vertices $x$; perhaps this remains true w…

The uniqueness conjecture. Then $u=u_3$. The inequalities need not be uniform in $z$.

Fix a polystable negative valuation $v$ on $X$. Let $\mathcal M_v$ be the space of compatible Calabi–Yau metrics on $X$ with $v=v_\omega$, let $\mathcal C_v$ be the corresponding w…

Let $f_{\rm in}$ be the initial datum in the setting of the paper's Landau weak-strong uniqueness theorem, and let $L^{\infty,k}$ denote the weighted bounded space used there. The…

Almost-everywhere uniqueness conjecture. For all vectors ${\bm b}\in\mathbb{R}^m$ except for a measure zero set, this program has a unique solution. The real analogue is establishe…

Let $\phi$ be a pair potential satisfying assumptions (A2) and (A3), with activity $z$ and inverse temperature $\beta$. A Gibbs measure is a probability measure describing the equi…

Uniqueness conjecture. For every $r\in(-1,1)$, there is a unique $\tau$ with $\operatorname{Re}\tau=r$ that solves the period condition for $\mathcal{T}$ with pitch $1$. For every…

Consider mean curvature flows starting from embedded two-spheres and allowing singularities. Uniqueness conjecture for mean curvature flow of embedded two-spheres. The mean curvatu…

Let equation be the complex matrix equation and equation its associated real matrix equation. Denote the real representation of a solution $X$ by $X_{\sigma}$. Uniqueness-correspon…

The uniqueness conjecture. Such a solution $u(t)$ cannot possess another solution $v(t)$ satisfying these initial conditions.

Uniqueness conjecture. Then $\lambda_1=\lambda_2$ and $r_2=r_1(\cdot+\xi)$ for some $xi\in\mathbb{R}^3$.

McKenna's uniqueness conjecture. Under these assumptions, there exists a unique large solution. This conjecture concerns uniqueness for boundary blow-up problems under the conditio…

Let $n$ be a positive integer, let $S\subset\mathbb{R}^n$, and let $f$ be compactly supported. A set $S$ is a non-uniqueness set for compactly supported functions $f$ if the corres…