Journal article
Sharp eigenvalue estimates on degenerating surfaces
- Abstract:
- We consider the first non-zero eigenvalue λ1 of the Laplacian on hyperbolic surfaces for which one disconnecting collar degenerates and prove that 8π∇ log(λ1) essentially agrees with the dual of the differential of the degenerating Fenchel-Nielsen length coordinate. As a consequence, we can improve previous results of Schoen, Wolpert, Yau [33] and Burger [6] to obtain estimates with optimal error rates and obtain new information on the leading order terms of the polyhomogeneous expansion of λ1 of Albin, Rochon and Sher
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 508.9KB, Terms of use)
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- Publisher copy:
- 10.1080/03605302.2019.1581805
Authors
- Publisher:
- Taylor and Francis
- Journal:
- Communications in Partial Differential Equations More from this journal
- Volume:
- 44
- Issue:
- 7
- Pages:
- 573-612
- Publication date:
- 2019-04-01
- Acceptance date:
- 2019-01-21
- DOI:
- EISSN:
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1532-4133
- ISSN:
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0360-5302
- Pubs id:
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pubs:968692
- UUID:
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uuid:800c0888-6a18-4999-a699-5ba0320048f5
- Local pid:
-
pubs:968692
- Source identifiers:
-
968692
- Deposit date:
-
2019-02-04
- ARK identifier:
Terms of use
- Copyright holder:
- Taylor & Francis Group, LLC
- Copyright date:
- 2019
- Rights statement:
- © 2019 Taylor & Francis Group, LLC.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Taylor and Francis at: https://doi.org/10.1080/03605302.2019.1581805
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