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arXiv · 1011.0535

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

Kingshook Biswas·Ricardo Perez-Marco
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Abstract

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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Kingshook Biswas, Ricardo Perez-Marco. 2010-11-02. Caratheodory convergence of log-Riemann surfaces and Euler's formula. https://arxiv.org/abs/1011.0535

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