The subelliptic heat kernels of the quaternionic Hopf fibration

21 Aug 2015  ·  Baudoin Fabrice, Wang Jing ·

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. read more

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Analysis of PDEs Mathematical Physics Differential Geometry Mathematical Physics Spectral Theory