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Infinitesimal aspects of the Laplace operator. (English) Zbl 1026.18007
Summary: In the context of synthetic differential geometry, we study the Laplace operator on a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the second neighbourhood usually required as support for second-order differential operators. The new neighbourhood has the property that a function is affine on it if and only if it is harmonic.

MSC:
18F15 Abstract manifolds and fiber bundles (category-theoretic aspects)
53B20 Local Riemannian geometry
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