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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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Estimate for the diameter of the image of a holomorphic disk by the area of the holomorphic ...

Let $(M, J, g)$ be a compact almost complex manifold with a Riemannian metric $g$ that preserves the almost complex structure $J$. I want to prove that a holomorphic disk $u: D^2\to M$ of a small area …