Author

Congpei An

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Preprint Sep 2026

Exact Finite Integral Geometry: Directional Kernels and Spherical Designs

We study when an invariant directional average from integral geometry can be replaced exactly by finitely many directions. For an even continuous kernel $\psi:[-1,1]\to\R$, let $T_\psi$ be the associated zonal convolution operator on the sphere and let $\cB_\psi K$ be the corresponding surface-area observable of a conv...

Cong-Pei An · 0 citations

Preprint Aug 2026

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

Let $X_N=\{x_1,\dots,x_N\}\subset \Sph^2$ be a spherical $t$-design of strength $t\ge2$, and let $\mu_X$ be its empirical measure. Minkowski's theorem associates with $X_N$ a convex polytope $P_X\subset\R^3$, unique up to translation, whose facet normals are the design nodes and whose facets all have area $4\pi/N$; equ...

Cong-Pei An · 2 citations