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What is Learnable in Valiant's Theory of the Learnable? 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Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
Hau-tieng Wu · 2013-05-18 · via math.ST updates on arXiv.org

Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on the tangent bundle. As a result, we can construct a distance in this class which leads to a pre-compactness theorem on the class under consideration.

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