Asymptotically optimal cubature formulas on manifolds for prefixed weights

TL;DR

This paper extends the proof of the Korevaar-Meyers conjecture to develop asymptotically optimal cubature formulas with fixed weights on algebraic and Riemannian manifolds, advancing numerical integration methods.

Contribution

It introduces a new approach to prove the conjecture for cubature formulas with prefixed weights on manifolds, expanding existing theoretical frameworks.

Findings

Established asymptotically optimal cubature formulas with fixed weights

Extended the proof of the Korevaar-Meyers conjecture to new settings

Provided theoretical foundations for numerical integration on manifolds

Abstract

We propose a new extension of the proof of the Korevaar-Meyers conjecture by Bondarenko, Radchenko and Viazovska for cubature formulas with prefixed weights (we fix different weights for different points) on algebraic and Riemannian manifolds.