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  • Print publication year: 2019
  • Online publication date: October 2019

21 - The Sub-Riemannian Heat Equation


In this chapter we derive the sub-Riemannian heat equation and its relation to the notion of intrinsic volume in sub-Riemannian geometry. We then discuss (without proof) the Hörmander theorem. In the last part of the chapter we present an elementary method to compute the fundamental solution of the heat equation on the Heisenberg group (the celebrated Gaveau–Hulanicki formula).

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