Geodesic
The coarea inequality
Behnam Esmayli1 ; Piotr Hajłasz1
1University of Pittsburgh, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 965-991
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  The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all details. The known proof is based on a difficult result of Davies. Our proof is elementary and does not use Davies' theorem. Instead we use an elegant argument that we learned from Nazarov through MathOverflow. We also obtain some generalizations of the coarea inequality.
Keywords: Metric spaces, Hausdorff measure, coarea inequality

Behnam Esmayli  1   ; Piotr Hajłasz  1

1 University of Pittsburgh, Department of Mathematics 
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Behnam Esmayli; Piotr Hajłasz. The coarea inequality. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 965-991. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a21/