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Recently, the study of (singular) surfaces with λ<2, but not of Hecke's form has been undertaken by C. M. [Judge] in connection with the Lax-Phillips work on the Roelcke-Selberg Conjecture
These natural expansions of the limit set were recently re-discovered by [Pignataro] in her 1986 thesis. She used them to study the Hausdorff dimension of the limit set ofG q when λ>2 (andG q is of the second kind.)
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Schmidt, T.A., Sheingorn, M. Length spectra of the Hecke triangle groups. Math Z 220, 369–397 (1995). https://doi.org/10.1007/BF02572621
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DOI: https://doi.org/10.1007/BF02572621