3 problems

Let $\Omega\subset\mathbb{R}^N$ be a bounded domain, let $\mu_1(\Omega)\leq\mu_2(\Omega)\leq\cdots$ denote its first nontrivial Neumann eigenvalues of the Ornstein–Uhlenbeck operat…

Let $\Omega_0$ and $\Omega_1$ be convex sets containing the origin, and let $\Omega_t=(1-t)\Omega_0+t\Omega_1$ for $t\in[0,1]$. The Gaussian measure is denoted by $\gamma$. Garcia-…

Let $p(x,z;t)$ be the Mehler kernel of the Ornstein–Uhlenbeck semigroup, defined for $t>0$ and $(x,z)\in\mathbb R^n\times\mathbb R^n$ by … The kernel $p$ is log-concave in $(x,z)$.…