On the heat kernel of the Rumin complex and Calderón reproducing formula

2023/05/17 by Ciatti, Paolo, Franchi, Bruno, Sire, Yannick
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.10493

Abstract

We derive several properties of the heat equation with the Hodge operator associated with the Rumin complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin's differential forms to construct a Calderón reproducing formula on Rumin forms.

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