6 problems

Let $k\geq 1$, $d\geq 1$, and let $u=u(t,x_1,\dots,x_k,v)$ be a nonnegative weak subsolution of … Set … … and define…

Let $G=(V,E)$ be a graph with degree bound $d_*$, and let $B(x,r)$ denote the open ball of radius $r$ about $x$. Assume the degree and curvature hypotheses referred to as Assumptio…

Let $g(t)=\exp(t-e^t)$, and let $\gamma(x,\xi)=\exp(-a|x|-b|\xi|)$ with $a,b>0$. Suppose that $f\in L^2(\mathbb{R})$ has exponential time-frequency concentration, meaning … Let…

Let $\mu$ be a centered and isotropic probability measure on $\mathbb{R}^n$ with density $d\mu=e^{-\phi}dx$, meaning … Let $\gamma$ denote the standard Gaussian measure, and let…

Let $w$ be a weight in $A_{p,\mathfrak{R}}$ for $p>1$. For a rectangle $R=I_1\times I_2$, let $\pi_R(f)$ denote the projection used in the Poincaré inequality, and let…

Coarse total vertical perimeter conjecture. For every measurable $A\subseteq\mathbb H(\mathbb R)$ and every $\varepsilon\in(0,1/2)$,