Abstract
In this note, we obtain some De Lellis–Top** type inequalities for general tensors under some assumptions of the Bakry–Émery Ricci tensor. In particular, we provide new results on weighted manifolds with convex boundary, generalizing some known results on manifolds with boundary. Furthemore, we apply our results to a special class of locally conserved tensors.
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Acknowledgements
The authors would like to thank the Professor Jia-Yong Wu for making several relevant comments and suggestions in a previous version of this work. This work is a part of the Ph.D. thesis of the first author.
Funding
This work was funded by the public call n. 03 Produtividade em Pesquisa proposal code PIA13495-2020 and it was partially supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil [CAPES: Finance code - 001 to second and third authors].
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Cruz, F., Freitas, A. & Santos, M. De Lellis–Top** Inequalities on Weighted Manifolds with Boundary. Results Math 77, 16 (2022). https://doi.org/10.1007/s00025-021-01549-5
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DOI: https://doi.org/10.1007/s00025-021-01549-5