The authors establish weighted Minkowski inequalities and quantitative stability for weighted Alexandrov-Fenchel inequalities for nearly spherical sets in space forms using convex weights.
Maggi, Some methods for studying stability in isoperimetric type problems, Bulletin of the Amer- ican Mathematical Society, 2008, 45(3): 367-408
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On the new weighted geometric inequalities near the sphere in space forms
The authors establish weighted Minkowski inequalities and quantitative stability for weighted Alexandrov-Fenchel inequalities for nearly spherical sets in space forms using convex weights.