Gradient estimates for the heat kernels in higher dimensional Heisenberg groups

Abstract

The author obtains sharp gradient estimates for the heat kernels in two kinds of higher dimensional Heisenberg groups — the non-isotropic Heisenberg group and the Heisenberg type group ℍ _n,m. The method used here relies on the positive property of the Bakry-Émery curvature Γ₂ on the radial functions and some associated semigroup technics.

Keywords

Gradient estimates / Γ₂ curvature / Heat kernels / Sublaplace / Heisenberg group

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