The authors establish weighted Minkowski inequalities and quantitative stability for weighted Alexandrov-Fenchel inequalities for nearly spherical sets in space forms using convex weights.
Solanes, Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces , Trans- actions of the American Mathematical Society, 2006, 358(3): 1105-1115
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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.