Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces
In the previous work (Zhang and Zhu in J Differ Geom, http://arxiv.org/pdf/1012.4233v3, 2012), the second and third authors established a Bochner type formula on Alexandrov spaces. The purpose of this paper is to give some applications of the Bochner type formula. Firstly, we extend the sharp lower...
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1826289000920383488 |
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| author | Qian, Z Zhang, H Zhu, X |
| author_facet | Qian, Z Zhang, H Zhu, X |
| author_sort | Qian, Z |
| collection | OXFORD |
| description | In the previous work (Zhang and Zhu in J Differ Geom, http://arxiv.org/pdf/1012.4233v3, 2012), the second and third authors established a Bochner type formula on Alexandrov spaces. The purpose of this paper is to give some applications of the Bochner type formula. Firstly, we extend the sharp lower bound estimates of spectral gap, due to Chen and Wang (Sci Sin (A) 37:1-14, 1994), Chen and Wang (Sci Sin (A) 40:384-394, 1997) and Bakry-Qian (Adv Math 155:98-153, 2000), from smooth Riemannian manifolds to Alexandrov spaces. As an application, we get an Obata type theorem for Alexandrov spaces. Secondly, we obtain (sharp) Li-Yau's estimate for positve solutions of heat equations on Alexandrov spaces. © 2012 Springer-Verlag. |
| first_indexed | 2024-03-07T02:22:14Z |
| format | Journal article |
| id | oxford-uuid:a456fe07-bb97-4fec-ab44-0c67faf313d6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:22:14Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:a456fe07-bb97-4fec-ab44-0c67faf313d62022-03-27T02:33:10ZSharp spectral gap and Li-Yau's estimate on Alexandrov spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a456fe07-bb97-4fec-ab44-0c67faf313d6EnglishSymplectic Elements at Oxford2013Qian, ZZhang, HZhu, XIn the previous work (Zhang and Zhu in J Differ Geom, http://arxiv.org/pdf/1012.4233v3, 2012), the second and third authors established a Bochner type formula on Alexandrov spaces. The purpose of this paper is to give some applications of the Bochner type formula. Firstly, we extend the sharp lower bound estimates of spectral gap, due to Chen and Wang (Sci Sin (A) 37:1-14, 1994), Chen and Wang (Sci Sin (A) 40:384-394, 1997) and Bakry-Qian (Adv Math 155:98-153, 2000), from smooth Riemannian manifolds to Alexandrov spaces. As an application, we get an Obata type theorem for Alexandrov spaces. Secondly, we obtain (sharp) Li-Yau's estimate for positve solutions of heat equations on Alexandrov spaces. © 2012 Springer-Verlag. |
| spellingShingle | Qian, Z Zhang, H Zhu, X Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces |
| title | Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces |
| title_full | Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces |
| title_fullStr | Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces |
| title_full_unstemmed | Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces |
| title_short | Sharp spectral gap and Li-Yau's estimate on Alexandrov spaces |
| title_sort | sharp spectral gap and li yau s estimate on alexandrov spaces |
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