English

The subelliptic heat kernels of the quaternionic Hopf fibration

Analysis of PDEs 2015-08-24 v2 Mathematical Physics Differential Geometry math.MP Spectral Theory

Abstract

The main goal of this work is to study the sub-Laplacian of the unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the quaternionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of the conformal sub-Laplacian and small-time asymptotics. As a byproduct of our study we also obtain several results related to the sub-Laplacian of a projected Hopf fibration.

Keywords

Cite

@article{arxiv.1310.5938,
  title  = {The subelliptic heat kernels of the quaternionic Hopf fibration},
  author = {Fabrice Baudoin and Jing Wang},
  journal= {arXiv preprint arXiv:1310.5938},
  year   = {2015}
}

Comments

A typo in Proposition 2.4 noted by Luca Rizzi has been corrected