Infinitesimal aspects of the Laplace operator

Details Infinitesimal aspects of the Laplace operator Infinitesimal aspects of the Laplace operator

2000-06-23

arxiv.org/abs/math/0006180v1

Mathematics

Category Theory

19 pages

Scientific paper

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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