θ-horocap-convex capillary hypersurfaces in the unit ball satisfy the full quermassintegral inequalities via convergence of a Guan-Li type curvature flow with capillary boundary.
The quermassintegral inequalities for horo-convex domains in the sphere
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Reverse Alexandrov-Fenchel and Heintze-Karcher inequalities are proved with deficits controlled by oriented volumes of focal maps, yielding sharp estimates in Minkowski planes, Euclidean space, spheres, and hyperbolic space.
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Capillary quermassintegral inequalities in the unit ball
θ-horocap-convex capillary hypersurfaces in the unit ball satisfy the full quermassintegral inequalities via convergence of a Guan-Li type curvature flow with capillary boundary.
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Heintze-Karcher and Reverse Alexandrov-Fenchel Inequalities via Focal Geometry
Reverse Alexandrov-Fenchel and Heintze-Karcher inequalities are proved with deficits controlled by oriented volumes of focal maps, yielding sharp estimates in Minkowski planes, Euclidean space, spheres, and hyperbolic space.