22/06/05 14:37:15 n5vX6CbC.net
>>128
つづき
(参考)
URLﾘﾝｸ(ja.wikipedia.org)
リーマン面
URLﾘﾝｸ(en.wikipedia.org)
Riemann surface
Ramified covering spaces
Continuing in this vein, compact Riemann surfaces can map to surfaces of lower genus, but not to higher genus, except as constant maps. This is because holomorphic and meromorphic maps behave locally like z → z^n, so non-constant maps are ramified covering maps, and for compact Riemann surfaces these are constrained by the Riemann?Hurwitz formula in algebraic topology, which relates the Euler characteristic of a space and a ramified cover.
For example, hyperbolic Riemann surfaces are ramified covering spaces of the sphere (they have non-constant meromorphic functions), but the sphere does not cover or otherwise map to higher genus surfaces, except as a constant.
URLﾘﾝｸ(en.wikipedia.org)
Schottky's theorem
Several authors, such as Jenkins (1955), have given variations of Ahlfors's bound with better constants: in particular Hempel (1980) gave some bounds whose constants are in some sense the best possible.
(引用終り)
以上