Stability of Alexandrov–Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms

Zhou, Rong; Zhou, Tailong

doi:10.1007/s12220-024-01794-4

J Geom Anal

2024

DOI: 10.1007/s12220-024-01794-4

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Stability of Alexandrov–Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms

Rong Zhou,

Tailong Zhou

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Stability of the Quermassintegral Inequalities in Hyperbolic Space

Sahjwani,

Scheuer

2023

J Geom Anal

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For the quermassintegral inequalities of horospherically convex hypersurfaces in the $$(n+1)$$ ( n + 1 ) -dimensional hyperbolic space, where $$n\ge 2$$ n ≥ 2 , we prove a stability estimate relating the Hausdorff distance to a geodesic sphere by the deficit in the quermassintegral inequality. The exponent of the deficit is explicitly given and does not depend on the dimension. The estimate is valid in the class of domains with upper and lower bound on the inradius and an upper bound on a curvature quotient. This is achieved by some new initial value-independent curvature estimates for locally constrained flows of inverse type.

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Stability of the Quermassintegral Inequalities in Hyperbolic Space

Sahjwani,

Scheuer

2023

J Geom Anal

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Stability of Alexandrov–Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms

Cited by 1 publication

References 25 publications

Stability of the Quermassintegral Inequalities in Hyperbolic Space

Stability of the Quermassintegral Inequalities in Hyperbolic Space

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