Optimal asymptotic bounds for designs on manifolds

Abstract

We extend to the case of a $d$-dimensional compact connected oriented Riemannian manifold $\mathcal{M}$ the theorem of A. Bondarenko, D. Radchenko and M. Viazovska on the existence of $L$-designs consisting of $N$ nodes, for any $N\ge C_{\mathcal{M}}{L}^d$. For this, we need to prove a version of the Marcinkiewicz-Zygmund inequality for the gradient of diffusion polynomials.

arXiv comment21 pages

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Cited by in corpus (3)

• Graphical Designs and Extremal Combinatorics
• An enhanced uncertainty principle for the Vaserstein distance
• Sampling theorems for inverse problems on Riemannian manifolds