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arXiv · 2405.08605

On gradient estimates of the heat semigroups on step-two Carnot groups

Sheng-Chen Mao·Ye Zhang
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Abstract

In this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry-\'Emery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three generators $N_{3,2}$. Moreover, high order gradient estimates and the Riemannian counterparts are also deduced under an extra condition.

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Sheng-Chen Mao, Ye Zhang. 2024-05-14. On gradient estimates of the heat semigroups on step-two Carnot groups. https://doi.org/10.1007/s11118-025-10222-3

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