Download L² Approaches in Several Complex Variables: Development of by Takeo Ohsawa PDF

By Takeo Ohsawa

The objective of this monograph is to provide the present prestige of a swiftly constructing a part of numerous advanced variables, prompted by means of the applicability of potent effects to algebraic geometry and differential geometry. Highlighted are the hot special effects at the L² extension of holomorphic functions.

In bankruptcy 1, the classical questions of a number of advanced variables motivating the improvement of this box are reviewed after priceless arrangements from the fundamental notions of these variables and of complicated manifolds similar to holomorphic capabilities, pseudoconvexity, differential kinds, and cohomology. In bankruptcy 2, the L² approach to fixing the d-bar equation is gifted emphasizing its differential geometric element. In bankruptcy three, a refinement of the Oka–Cartan idea is given through this system. The L² extension theorem with an optimum consistent is incorporated, acquired lately via Z. Błocki and via Q.-A. Guan and X.-Y. Zhou individually. In bankruptcy four, numerous effects at the Bergman kernel are offered, together with fresh works of Maitani–Yamaguchi, Berndtsson, and Guan–Zhou. almost all these effects are acquired through the L² approach. within the final bankruptcy, really particular effects are mentioned at the life and class of yes holomorphic foliations and Levi flat hypersurfaces as their stables units. those also are purposes of the L² strategy bought in the course of those 15 years.

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