Abstract
We prove height estimates concerning compact hypersurfaces with nonzero constant weighted mean curvature and whose boundary is contained into a slice of a weighted product space of nonnegative Bakry–Émery–Ricci curvature. As applications of our estimates, we obtain half-space type results related to complete noncompact hypersurfaces properly immersed in such an ambient space.
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Acknowledgements
The first author is partially supported by CNPq, Brazil, Grant 303977/2015-9. The authors would like to thank the referee for giving valuable suggestions and comments which improved the paper.
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de Lima, H.F., Santos, M.S. Height estimates and half-space type theorems in weighted product spaces with nonnegative Bakry–Émery–Ricci curvature. Ann Univ Ferrara 63, 323–332 (2017). https://doi.org/10.1007/s11565-016-0268-5
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DOI: https://doi.org/10.1007/s11565-016-0268-5
Keywords
- Weighted product spaces
- Bakry–Émery–Ricci tensor
- Compact hypersurfaces
- Height estimates
- Half-space type theorems