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# Arithmeticity, Discreteness and Volume

@inproceedings{Gehring1997ArithmeticityDA, title={Arithmeticity, Discreteness and Volume}, author={Frederick W. Gehring}, year={1997} }

- Published 1997

We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of PSL(2, c). We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between elliptic axes. We establish the discreteness and arithmeticity of a number of these extremal groups… CONTINUE READING