Analytic maps between Riemann surfaces
نویسندگان
چکیده
منابع مشابه
Harmonic maps from degenerating Riemann surfaces
We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in W 1,2 and C modulo bubbles of sequences of such maps. 2000 Mathematics Subject Classification: 58E20
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Example 1.2. (a) Suppose X is a Riemann surface. Let Y ⊂ X be a (connected) open subset. Then Y is a Riemann surface, whose complex structure is given by taking all U ⊂ Y from charts of X. (b) Let P = C ∪ {∞}, homeomorphic to the real sphere. Take U1 = P\{∞} = C, U2 = P\{0} = C∗ ∪ {∞}. Define φ1(z) = z, φ2(z) = 1/z for z 6= ∞ and φ2(∞) = 0. Then φ2 ◦ φ−1 1 : C∗ → C∗ is given by z 7→ 1/z, which ...
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The problem of mapping between two non-isometric surfaces admits ambiguities on both local and global scales. For instance, symmetries can make it possible for multiple maps to be equally acceptable, and stretching, slippage, and compression introduce difficulties deciding exactly where each point should go. Since most algorithms for point-to-point or even sparse mapping struggle to resolve the...
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Penrose's twistor theory and many other ideas of mathematical physics are based on the notion of complexification. This notion is explained and examples of its apphcation in physics and mathematics are described. In particular, the well-known analogy between Yang-Mills fields and harmonic maps of Riemann surfaces becomes rather stronger after complexification. This strengthening is the main poi...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1962
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1962-0136725-1