Stability of the quermassintegral inequalities in hyperbolic space

Sahjwani, Prachi and Scheuer, Julian 2023. Stability of the quermassintegral inequalities in hyperbolic space. Journal of Geometric Analysis 34 , 13. 10.1007/s12220-023-01453-0

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Abstract

For the quermassintegral inequalities of horospherically convex hypersurfaces in the (n + 1)-dimensional hyperbolic space, where 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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	1050-6926
Funders:	Engineering and Physical Sciences Research Council
Date of First Compliant Deposit:	2 October 2023
Date of Acceptance:	25 September 2023
Last Modified:	02 Nov 2023 12:21
URI:	https://orca.cardiff.ac.uk/id/eprint/162868

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