3 problems

Let $(B^{n+1},dx^2)$ be the unit ball in Euclidean $(n+1)$-space, and let $k=\frac{n+1}{2}$. Define … For $g=e^{2u}dx^2$, let $\mathcal{F}_k(g)$ denote the critical conformal primi…

Let $h^{\infty}$ denote the space of bounded harmonic functions on the unit ball $\mathbb{B}^n:=\{x\in\mathbb{R}^n:|x|<1\}$. For $x\in\mathbb{B}^n$ and $l\in\mathbb{S}^{n-1}$, let…

Let $d\geq 3$. The quantity $\mathcal S_d$ denotes the supremum in the relevant paraboloid extension inequality over functions $\psi$ on $\mathbb{R}^d$. Foschi's Gaussian maximizer…