Infinitesimal aspects of the Laplace operator
Theory and Applications of Categories [electronic only] , CT2000, Tome 9 (2000), pp. 1-16.

Voir la notice de l'article dans Theory and Applications of Categories website

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.
Classification : 18F99, 53B20.
Mots-clés : Laplacian, harmonic, conformal, synthetic dfferential geometry. 
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     author = {Anders Kock},
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Anders Kock. Infinitesimal aspects of the Laplace operator. Theory and Applications of Categories [electronic only]
, CT2000, Tome 9 (2000), pp. 1-16. https://geodesic-test.mathdoc.fr/item/TAC_2000__9_a0/