2 problems

Let $\Omega\subset \mathbb{R}^d$ be an open bounded set with smooth boundary, and let … be its heat content with respect to the Poisson kernel. Acuna's heat-content perimeter conje…

Let $N$ be a nilpotent group, and let $P^\sigma(t,0)$ denote the Poisson kernel associated with the setting above. The preceding theorem gives an estimate for $P^\sigma(t,0)(x)$ on…