Abstract
We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson–Walker spaces satisfying the null convergence condition.
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Acknowledgements
This work was made possible through a research scholarship JS received from the DFG and which was carried out at Columbia University in New York. JS would like to thank the DFG, Columbia University and especially Prof. Simon Brendle for their support.
The authors would like to thank Prof. Mu-Tao Wang for an interesting discussion.
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BL was supported by Leverhulme Trust Research Project Grant RPG-2016-174. The work of JS was funded by the “Deutsche Forschungsgemeinschaft” (DFG, German research foundation); Project “Quermassintegral preserving local curvature flows”; Grant number SCHE 1879/3-1.
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Lambert, B., Scheuer, J. Isoperimetric problems for spacelike domains in generalized Robertson–Walker spaces. J. Evol. Equ. 21, 377–389 (2021). https://doi.org/10.1007/s00028-020-00584-z
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DOI: https://doi.org/10.1007/s00028-020-00584-z