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- W2952883669 abstract "We consider different sub-Laplacians on a sub-Riemannian manifold $M$. Namely, we compare different natural choices for such operators, and give conditions under which they coincide. One of these operators is a sub-Laplacian we constructed previously in cite{GordinaLaetsch2014a}. This operator is canonical with respect to the horizontal Brownian motion, we are able to define the sub-Laplacian without some a priori choice of measure. The other operator is $operatorname{div}^{omega} operatorname{grad}_{mathcal{H}}$ for some volume form $omega$ on $M$. We illustrate our results by examples of three Lie groups equipped with a sub-Riemannian structure: $operatorname{SU}left( 2 right)$, the Heisenberg group and the affine group." @default.
- W2952883669 created "2019-06-27" @default.
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- W2952883669 date "2014-11-29" @default.
- W2952883669 modified "2023-09-23" @default.
- W2952883669 title "Sub-Laplacians on sub-Riemannian manifolds" @default.
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