Journal article
Heat flows on hyperbolic spaces
- Abstract:
- In this paper we develop new methods for studying the convergence problem for the heat flow on negatively curved spaces and prove that any quasiconformal map of the sphere Sn−1, n ≥ 3, can be extended to the n-dimensional hyperbolic space such that the heat flow starting with this extension converges to a quasi-isometric harmonic map. This implies the Schoen–Li–Wang conjecture that every quasiconformal map of Sn−1, n ≥ 3, can be extended to a harmonic quasi-isometry of the n-dimensional hyperbolic space.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
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(Preview, Accepted manuscript, 665.7KB, Terms of use)
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- Publisher copy:
- 10.4310/jdg/1519959624
Authors
- Publisher:
- International Press
- Journal:
- Journal of Differential Geometry More from this journal
- Volume:
- 108
- Issue:
- 3
- Pages:
- 495-529
- Publication date:
- 2018-03-02
- Acceptance date:
- 2018-01-15
- DOI:
- EISSN:
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1945-743X
- ISSN:
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0022-040X
- Language:
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English
- Keywords:
- Pubs id:
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1109985
- Local pid:
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pubs:1109985
- Deposit date:
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2020-10-17
Terms of use
- Copyright holder:
- International Press of Boston, Inc.
- Copyright date:
- 2018
- Rights statement:
- © 2018 by International Press of Boston, Inc. All rights reserved.
- Notes:
-
This is the accepted manuscript version of the article. The final version is available from International Press at https://doi.org/10.4310/jdg/1519959624
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