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SUMMARY:Sharp eigenvalue estimates on degenerating surfaces. - Melanie Rup
 flin\, University of Oxford
DTSTART:20190128T150000Z
DTEND:20190128T160000Z
UID:TALK109627@talks.cam.ac.uk
CONTACT:Ivan Moyano
DESCRIPTION:We consider the first non-zero eigenvalue $\\lambda_1$ of the\
 nLaplacian on hyperbolic surfaces for which one disconnecting collar\ndege
 nerates and show that the gradient of $\\lambda_1$ is given\nessentially e
 xplicitly in terms of the dual of the differential of the\ndegenerating le
 ngth coordinate. As a corollary we obtain sharp error\nestimates on  $\\la
 mbda_1$ that improve previous results of Burger and\nSchoen-Wolpert-Yau an
 d provide new information on the second term in the\npolyhomogenous expans
 ion of $\\lambda_1$. The presented results are joint\nwork with Nadine Gro
 sse.
LOCATION:CMS\, MR13
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