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Li Ma and Baiyu Liu
Convexity of the first eigenfunction of the drifting Laplacian operator and its applications
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| Published: |
August 30, 2008
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| Keywords: |
Convexity, first eigenfunction, drifting Laplacian, warped product |
| Subject: |
35C44 |
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Abstract
In this short note, we prove the convexity of the first
eigenfunction of the drifting Laplacian operator with zero Dirichlet
boundary value provided a suitable assumption to the drifting term
is added. After giving a gradient estimate, we then use the
convexity of the first eigenfunction to get a lower bound of the
difference of the first and second eigenvalues of the drifting
Laplacian.
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| Acknowledgements
This research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20060003002
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| Author information
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
lma@math.tsinghua.edu.cn
liuby05@mails.tsinghua.edu.cn
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