Abstract
In the main result the stability of euclidean balls with one pinched curvature measure is proved giving an explicit stability order which depends only on the dimension of the ambient space. Stability here is meant with respect to the Hausdorff measure for compact convex bodies. The technique of the proof involves generalized Minkowski integral formulas, inner parallel bodies and estimates for the isoperimetric defect. The result also improves stability estimates for orthogonal disc cylinders in the noncompact case.
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Kohlmann, P. Curvature measures and stability. J Geom 68, 142–154 (2000). https://doi.org/10.1007/BF01221068
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DOI: https://doi.org/10.1007/BF01221068