By M. Salah Baouendi
This publication offers some of the major advancements of the earlier twenty years within the examine of actual submanifolds in advanced house, supplying the most important history fabric for researchers and complex graduate scholars. The concepts during this region borrow from genuine and complicated research and partial differential equations, in addition to from differential, algebraic, and analytical geometry. In flip, those latter components were enriched through the years via the learn of difficulties in numerous advanced variables addressed the following. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, contain large initial fabric to make the publication available to nonspecialists.
One of an important issues that the authors handle here's the holomorphic extension of services and mappings that fulfill the tangential Cauchy-Riemann equations on actual submanifolds. They current the most ends up in this region with a unique and self-contained method. The ebook additionally devotes significant cognizance to the research of holomorphic mappings among actual submanifolds, and proves finite decision of such mappings by way of their jets less than a few optimum assumptions. The authors additionally provide an intensive comparability of many of the nondegeneracy stipulations for manifolds and mappings and current new geometric interpretations of those stipulations. during the ebook, Cauchy-Riemann vector fields and their orbits play a valuable position and are awarded in a environment that's either common and elementary.
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