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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
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Question on PDEs which are related to certain geometric problems (e.g. Calabi conjecture, Ga...
For operator f(\lambda)=\log P_k(\lambda), in Guan Bo's several papers, say arXiv:1409.3633v1, Page 5 below Theorem 1.9, they mention some basic properties about it, such as it satisfies (1.2) to (1.6 …