The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of
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978-0-8218-4304-8 (9780821843048)
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Schweitzer Klassifikation
Review of foliation theory Foliated CR manifolds Levi foliations Levi foliations of CR submanifolds in $\mathbb{C}P^N$ Tangentially CR foliations Transversally CR foliations $\mathcal{G}$-Lie foliations Transverse Beltrami equations Review of orbifold theory Pseudo-differential operators on orbifolds Cauchy-Riemann orbifolds Holomorphic bisectional curvature Partition of unity on orbifolds Pseudo-differential operators on $\mathbb{R}^n$ Bibliography Index.
