2 problems

Let $n\geq 2$ be an integer. Let $K$ and $L$ be symmetric convex bodies in $\mathbb R^n$ containing the origin in their interiors. For $\lambda\in[0,1]$, define their geometric ave…

Let $K\in\mathcal{K}^2_{+,e}$ be an origin-symmetric convex body with smooth boundary and strictly positive curvature. Let $-\Delta_K$ be the associated centro-affine Laplacian, an…