Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
Differential Geometry
2018-05-10 v3 Analysis of PDEs
Abstract
We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the sub-Riemannian distance may be obtained as a limit of horizontal and vertical comparison theorems for the Riemannian distances approximations.
Keywords
Cite
@article{arxiv.1706.08489,
title = {Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations},
author = {Fabrice Baudoin and Erlend Grong and Kazumasa Kuwada and Anton Thalmaier},
journal= {arXiv preprint arXiv:1706.08489},
year = {2018}
}
Comments
Typos corrected, some improved bounds