Sharp eigenvalue estimates on degenerating surfaces

@inproceedings{Grosse2017SharpEE,
title={Sharp eigenvalue estimates on degenerating surfaces},
year={2017}
}
We consider the first non-zero eigenvalue $\lambda_1$ of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that $8\pi \nabla\log(\lambda_1)$ essentially agrees with the dual of the differential of the degenerating Fenchel-Nielson length coordinate. As a corollary of our analysis, which is based in particular on the fine properties of holomorphic quadratic differentials from the joint works of Topping and the second author, we can improve previous… CONTINUE READING
2

References

Publications referenced by this paper.
SHOWING 1-10 OF 15 REFERENCES

Asymptotic behavior of small eigenvalues , short geodesics and period matrices on degenerating hyperbolic Riemann surfaces

J. Huntley Grotowski, J. Jorgenson
• Forum Math .
• 2016

• 2015

Smooth long-time existence of Harmonic Ricci Flow on surfaces

• J. London Math. Society
• 2015

• 2009