1988/01/01 by Peter G. Doyle · 2 citations
Computer Science · Mathematics · Chemistry · #Topological and Geometric Data Analysis #Graph theory and applications #Mathematical Dynamics and Fractals #Bass (fish) #Mathematics #Group (periodic table) #Fishery #Chemistry #Biology
paper · pdf · doi:10.1007/bf02392277
openalex publication_date 1988/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using a classical method from physics called Rayleigh's cutting method, we prove the conjecture of Phillips and Sarnak that there is a universal lower bound L2> 0 for the lowest eigenvalue of the quotient manifold of a classical Schottky group acting on hyperbolic 3-space H 3. By work of Patterson and Sullivan, this implies that there is a universal upper bound U2 < 2 for the Hausdor dimension of the limit set of , or equivalently, for the critical exponent of the Poincare series associated with . The latter implication answers a question that can be traced back to Schottky and Burnside. 1