Jeffrey McGowan

most citedThe length of closed geodesics on random Riemann Surfaces

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math.DG2005★ 1 cited

The length of closed geodesics on random Riemann Surfaces

Eran Makover, Jeffrey McGowan

Short geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers' theorem gives a global bound on the length of the first $3 g - 3$ geodesics. We u…

math.DG2003

Bounds on Accumulation Rates of Eigenvalues on Manifolds with Degenerating Metrics

Jeffrey McGowan

We consider a family of manifolds with a class of degenerating warped product metrics $g_{ε} = ρ (ε, t)^{2 a} d t^{2} + ρ (ε, t)^{2 b} d s_{M}^{2}$ , with $M$ compact, $ρ$ homogeneous degree one, $a \le…