Ebook: The Sub-Laplacian Operators of Some Model Domains

The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker’s equations.

• A mathematically rigorous study of sub-Laplacian operators on some model domains in C^{n+1}.
• Presents the advanced theories in an easy-to-understand way.
• Of interest to researchers and graduate students working in analysis and geometry.