Spaces of Riemann Surfaces
Spaces of Riemann Surfaces
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In our eReader you can find the full English version of the book. Read Spaces of Riemann Surfaces Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Spaces of Riemann Surfaces
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, g, then iKA) e (k)^, ^. (li) If (^, X) e (e)^, and |A'| > |x. |, j = 1, ... , S, then (^:, X') e (if) . (ill) (h)^. „ is a domain. (iv) The inclusion (5) „ '^ ■^2n+- ^- ^^ ^^ sharp. (v) Every closed curve In y~ beginning in (H), ^ is homotoplc to a curve '■ — g, n v, ^ g, n in r?^ g, 3^ The proofs of (1) and (ii) are elementary; these statements impls^ easily (ill) and (Iv). The proof of (v) involves an explicit construction described below. The sharpness of (1) follows at once from (iv) and ...(v), 6, V/e prove now assertion (v) of g6 assviraing, for the sake of brevity, that g > 1, n = 0. Without loss of generality we may assiome that the given curve t — > (^(t), A(t)) e T„, o of class C^^ ; by hypothesis (^(0), X(0)) = (^(i), A(l)) e (e) ^ ^. UJ -^ g > o For each t we can find a standard fundamental region R°(t) belonging to (^(t), A(t)) such that the 2g boundary curves C. (t) of R (t) are real analytic and depend on t in a C manner, and such that 0°, ^(0) = C2.
What to read after Spaces of Riemann Surfaces?
You can find similar books in the "Read Also" column, or choose other free books by Lipman Bers to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, g, then iKA) e (k)^, ^. (li) If (^, X) e (e)^, and |A'| > |x. |, j = 1, ... , S, then (^:, X') e (if) . (ill) (h)^. „ is a domain. (iv) The inclusion (5) „ '^ ■^2n+- ^- ^^ ^^ sharp. (v) Every closed curve In y~ beginning in (H), ^ is homotoplc to a curve '■ — g, n v, ^ g, n in r?^ g, 3^ The proofs of (1) and (ii) are elementary; these statements impls^ easily (ill) and (Iv). The proof of (v) involves an explicit construction described below. The sharpness of (1) follows at once from (iv) and ...(v), 6, V/e prove now assertion (v) of g6 assviraing, for the sake of brevity, that g > 1, n = 0. Without loss of generality we may assiome that the given curve t — > (^(t), A(t)) e T„, o of class C^^ ; by hypothesis (^(0), X(0)) = (^(i), A(l)) e (e) ^ ^. UJ -^ g > o For each t we can find a standard fundamental region R°(t) belonging to (^(t), A(t)) such that the 2g boundary curves C. (t) of R (t) are real analytic and depend on t in a C manner, and such that 0°, ^(0) = C2.
What to read after Spaces of Riemann Surfaces?
You can find similar books in the "Read Also" column, or choose other free books by Lipman Bers to read onlineMoreLess
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