9 problems

Boundary curvature-integral conjecture. One has

Let $n$ be a positive integer, let $\operatorname{Curv}_k^\pm(\mathbb{R}^n)$ be the even or odd degree-$k$ curvature measures, and define … This is an invariant closed subspace und…

Let $n$ be a positive integer, let $\operatorname{Curv}_k(\mathbb{R}^n)$ be the degree-$k$ space of curvature measures with its topology induced by compact convergence, and let…

Let $X_i\in\text{Alex}^n(-1)$ be a sequence of Alexandrov spaces converging to $X$ in the Gromov–Hausdorff sense without collapsing. Let $\mu_{X_i}$ and $\mu_X$ denote their synthe…

Let $X\in\text{Alex}^n(-1)$, and let … be the synthetic curvature measure, where ${\operatorname R}$, $\mathcal{K}$, and $\theta$ are the corresponding density functions. Local fin…

Let $(M_i,g_i)$ be a sequence of $n$-dimensional manifolds with lower Ricci or sectional curvature bounds, and suppose that $M_i$ Gromov–Hausdorff converge without collapsing to…

Let $\phi$ be the norm defining the anisotropic curvature measures $\mathcal{C}_m^\phi(C,\cdot)$ of a convex body $C\subseteq\mathbf{R}^{n+1}$. Anisotropic curvature-measure charac…

Let $M$ be a Riemannian manifold. A valuation $\mu$ is called angular when … where $\mathcal{A}(M)$ is the space of angular curvature measures and $\cdot$ denotes the Alesker produ…

Let $M$ be a Riemannian manifold. The space of angular curvature measures is denoted by $\mathcal{A}(M)$, and the Lipschitz–Killing algebra by $\mathcal{L}\mathcal{K}(M)$. Here a v…