Greiner, Peter On second order hypoelliptic differential operators and the \(\overline\partial\)-Neumann problem. (English) Zbl 0747.58045 Complex analysis, Proc. Int. Workshop Ded. H. Grauert, Aspects Math. E 17, 134-142 (1991). [For the entire collection see Zbl 0722.00013.]Let \({\mathbf X}=\{X_ 1,\dots,X_ m\}\) be linearly independent vector fields in \(U\in\mathbb{R}^ n\), \(m\leq n\), and assume that finite many of \[ \{X_ i,[X_ j,X_ k],[X_ l,[X_ p,X_ q]],\dots\} \] generates \({\mathbf T}_ PU\) for all \(P\in U\). By Hörmander’s theorem the \({\mathbf X}\)- Laplacian \[ \Delta_{\mathbf X}=X^ 2_ 1+\cdots+X^ 2_ m \] is hypoelliptic. In the paper under review, the author computes the fundamental solutions for some examples and study the geometric meaning of the distance function yielded by the fundamental solutions. Reviewer: Lee Taichung (Hsinchu) Cited in 1 Document MSC: 58J10 Differential complexes 32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators 35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs Keywords:second-order hypoelliptic differential operators; fundamental solution; distance function; \(\overline\partial\)-Neumann problem Citations:Zbl 0722.00013 PDFBibTeX XMLCite \textit{P. Greiner}, in: Smooth proper modifications of compact Kähler manifolds. . 134--142 (1991; Zbl 0747.58045)