Dependence on dimension of a constant related to the Grötzsch ring

Abstract

For the constant λ n = lim a → 0 ( mod R G , n ( a ) + log ⁡ a ) {\lambda _n} = {\lim _{a \to 0}}(\bmod {R_{G,n}}(a) + \log a) associated with the Grötzsch extremal ring R G , n {R_{G,n}} in euclidean n n -space, we obtain the limit lim n → ∞ λ n 1 / n = e {\lim _{n \to \infty }}\lambda _n^{1/n} = e .