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arXiv · 1811.12676

Optimal asymptotic bounds for designs on manifolds

Bianca Gariboldi·Giacomo Gigante
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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.

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Bianca Gariboldi, Giacomo Gigante. 2018-11-30. Optimal asymptotic bounds for designs on manifolds. https://doi.org/10.2140/apde.2021.14.1701

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