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Infinitesimal aspects of the Laplace operator

Anders Kock
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Abstract

In the context of synthetic differential geometry, we study the Laplace operator an 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.

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Anders Kock. 2000-06-23. Infinitesimal aspects of the Laplace operator. https://arxiv.org/abs/math/0006180

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