Cong-Pei An

activity

20242026

collaborators

Showing 2026 · math.MGShow all

3 papers · 2 filters

math.MG2026

Exact Finite Integral Geometry: Directional Kernels and Spherical Designs

Congpei An

We study when an invariant directional average from integral geometry can be replaced exactly by finitely many directions. For an even continuous kernel $ψ : [- 1, 1] \to R$ , let $T_{ψ}$ …

math.MG2026

Dual Geometry of Spherical Designs: Polarity, Self-Polar Rigidity, and Quadrature Structure

Congpei An

Let $X=\{x_1,\ldots,x_N\}\subset\Sph^{d-1}$ be a spherical $t$ -design, $t \geq 2$ , and let $P_{X} \subset R^{d}$ be its Minkowski polytope. If $h_{i} = h_{P_{X}} (x_{i})$ , then \[ P_X^\circ=\conv\{…

math.MG2026

Minkowski Polytopes of Spherical Designs: High-Order Isotropy and Quantitative Sphericity

Congpei An

Let $X_N=\{x_1,\dots,x_N\}\subset \Sph^2$ be a spherical $t$ -design of strength $t \geq 2$ , and let $μ_{X}$ be its empirical measure. Minkowski's theorem associates with $X_{N}$ a convex…