Geometry of nonnegatively curved smooth metric measure spaces
- Degree Grantor:
- University of California, Santa Barbara. Mathematics
- Degree Supervisor:
- Guofang Wei
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2012
- Issued Date:
- 2012
- Topics:
- Mathematics and Applied Mathematics
- Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- Ph.D.--University of California, Santa Barbara, 2012
- Description:
In this dissertation we explore smooth metric measure spaces with nonnegative Bakry-Emery Ricci tensor. In particular, we prove a Liouville-type theorem for smooth metric measure spaces (M, g, e-f dvol ) with nonnegative Bakry-Emery Ricci tensor. This generalizes a result of Yau, which is recovered in the case f is constant. This result follows from a gradient estimate for f-harmonic functions on smooth metric measure spaces with Bakry-Emery Ricci tensor bounded from below. We also extend Zhong-Yang's first eigenvalue estimate to smooth metric measure spaces with nonnegative Bakry-Emery Ricci tensor and explore some aspects of a first eigenvalue estimate combining the Zhong-Yang and Lichnerowicz estimates.
- Physical Description:
- 1 online resource (49 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3545024
- ARK:
- ark:/48907/f3x63jv6
- ISBN:
- 9781267767219
- Catalog System Number:
- 990039147140203776
- Copyright:
- Kevin Brighton, 2012
- Rights:
- In Copyright
- Copyright Holder:
- Kevin Brighton
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