New York Journal of Mathematics
Volume 14 (2008) 393-401

  

Li Ma and Baiyu Liu

Convexity of the first eigenfunction of the drifting Laplacian operator and its applications


Published: August 30, 2008
Keywords: Convexity, first eigenfunction, drifting Laplacian, warped product
Subject: 35C44

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.

Acknowledgements

This research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20060003002


Author information

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
lma@math.tsinghua.edu.cn
liuby05@mails.tsinghua.edu.cn