Bull. Korean Math. Soc. 2023; 60(2): 325-338
Online first article January 26, 2023 Printed March 31, 2023
https://doi.org/10.4134/BKMS.b220120
Copyright © The Korean Mathematical Society.
Fanqi Zeng
Xinyang Normal University
In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincar\'{e}-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.
Keywords: Reilly-type inequality, generalized Ricci curvature, generalized mean curvature
MSC numbers: 53C21, 58J32
Supported by: This work was supported by NSFC (No.11971415), Natural Science Foundation of Henan (No.212300410235), and the Key Scientific Research Program in Universities of Henan Province (Nos.21A110021, 22A110021) and Nanhu Scholars Program for Young Scholars of XYNU (No.2019).
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