Injectivity Criteria for Holomorphic Curves in C
نویسنده
چکیده
Combining the definition of Schwarzian derivative for conformal mappings between Riemannian manifolds given by Osgood and Stowe with that for parametrized curves in Euclidean space given by Ahlfors, we establish injectivity criteria for holomorphic curves φ : D → C. The result can be considered a generalization of a classical condition for univalence of Nehari.
منابع مشابه
Math 8230, Spring 2010 Lecture Notes
1. Introductory remarks 1 2. Energy and area 3 3. Exact Lagrangian submanifolds and the non-squeezing theorem 7 4. Sobolev spaces 9 5. The linear Cauchy–Riemann operator 20 5.1. Proof of the Calderón–Zygmund Theorem for p , 2 26 6. Local properties of J-holomorphic curves 30 6.1. Smoothness 31 6.2. The Carleman Similarity Principle and its applications 35 6.3. Isolation of intersection points a...
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