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math.DG2014
Small eigenvalues of surfaces
Werner Ballmann, Henrik Matthiesen, Sugata Mondal
We show that the Laplacian of a Riemannian metric on a closed surface S with Euler characteristic χ(S) < 0 has at most -χ(S) small eigenvalues.
math.DG2014★ 3 cited
On topological upper-bounds on the number of small cuspidal eigenvalues
Sugata Mondal
Let be a noncompact, finite area hyperbolic surface of type . Let denote the Laplace operator on . As varies over the {\it moduli space} ${\mathcal{M}_{g,…
math.DG2014★ 6 cited
On largeness and multiplicity of the first eigenvalue of hyperbolic surfaces
Sugata Mondal
We apply topological methods to study the smallest non-zero number in the spectrum of the Laplacian on finite area hyperbolic surfaces. For closed hyperbolic surfaces of genu…