Infinitesimal aspects of the Laplace operator
Category Theory
2007-05-23 v1 Differential Geometry
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.
Cite
@article{arxiv.math/0006180,
title = {Infinitesimal aspects of the Laplace operator},
author = {Anders Kock},
journal= {arXiv preprint arXiv:math/0006180},
year = {2007}
}
Comments
19 pages