Rotational epi-symmetrization maximizes best outer-linearization approximations for monotone concave functionals on coercive convex functions.
Stochastic forms of brunn’s principle
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Establishes stochastic isoperimetric inequalities for functional quermassintegrals on random p-concave functions and proves that Zhang's affine Sobolev inequality holds in expectation under these models.
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Generalized outer linearizations and extremal properties of rotational epi-symmetrizations
Rotational epi-symmetrization maximizes best outer-linearization approximations for monotone concave functionals on coercive convex functions.
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On stochastic forms of functional isoperimetric inequalities
Establishes stochastic isoperimetric inequalities for functional quermassintegrals on random p-concave functions and proves that Zhang's affine Sobolev inequality holds in expectation under these models.