Caratheodory convergence of log-Riemann surfaces and Euler's formula

Details Caratheodory convergence of log-Riemann surfaces and Euler's formula Caratheodory convergence of log-Riemann surfaces and Euler's formula

2010-11-02

arxiv.org/abs/1011.0535v2

Mathematics

Complex Variables

Scientific paper

We define the notion of log-Riemann surfaces and Caratheodory convergence of
log-Riemann surfaces. We prove a convergence theorem for uniformizations of
simply connected log-Riemann surfaces converging in the Caratheodory topology.
We obtain as a corollary a purely geometric proof of Euler's formula (1 +
z/n)^n -> e^z .

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