By Giuseppe Zampieri
Cauchy-Riemann (CR) geometry is the research of manifolds built with a approach of CR-type equations. in comparison to the early days while the aim of CR geometry used to be to provide instruments for the research of the life and regularity of suggestions to the $\bar\partial$-Neumann challenge, it has swiftly got a lifetime of its personal and has turned a big subject in differential geometry and the examine of non-linear partial differential equations. an entire realizing of contemporary CR geometry calls for wisdom of assorted subject matters comparable to real/complex differential and symplectic geometry, foliation idea, the geometric concept of PDE's, and microlocal research. these days, the topic of CR geometry is particularly wealthy in effects, and the volume of fabric required to arrive competence is formidable to graduate scholars who desire to examine it. notwithstanding, the current ebook doesn't goal at introducing all of the themes of present curiosity in CR geometry. as a substitute, an test is made to be pleasant to the amateur through relocating, in a pretty comfy means, from the weather of the idea of holomorphic services in numerous complicated variables to complicated subject matters comparable to extendability of CR capabilities, analytic discs, their infinitesimal deformations, and their lifts to the cotangent house. the alternative of issues presents an excellent stability among a primary publicity to CR geometry and matters representing present study. Even a pro mathematician who desires to give a contribution to the topic of CR research and geometry will locate the alternative of issues beautiful
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