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Minimum sums of moments or, equivalently, distortion of optimum quantizers play an important role in several branches of mathematics. Fejes Toth's inequality for sums of moments in the plane and Zador's asymptotic formula for minimum distortion in Euclidean d-space are the first precise pertinent results in dimension d>=2. In this article these results are generalized in the form of asymptotic...
In this article we first extend Fejes Tóth's basic result on sums of moments from the plane to Riemannian 2-manifolds. The extension as well as the original result show that for certain geometric or analytic problems regular hexagonal arrangements are optimal or almost optimal. Then a stability counterpart of the moment theorem for Riemannian 2-manifolds is given. It shows that, conversely, for several...
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