The authors establish weighted Minkowski inequalities and quantitative stability for weighted Alexandrov-Fenchel inequalities for nearly spherical sets in space forms using convex weights.
Fuglede, Stability in the isoperimetric problem for convex or nearly spherical domains in Rn, Transactions of the American Mathematical Society, 1989, 314(2): 619-638
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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.