A sharp quantitative isoperimetric inequality in hyperbolic \(n\)-space

DOI10.1007/s00526-015-0928-9zbMath1336.49055OpenAlexW2210546041MaRDI QIDQ5963597

Verena Bögelein, Frank Duzaar, Christoph Scheven

Publication date: 22 February 2016

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-015-0928-9

zbMATH Keywords

\(L^2\)-oscillation indexFraenkel asymmetryhyperbolic \(n\)-spaceisoperimetric deficitquantitative isoperimetric inequality

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75) Non-Euclidean differential geometry (53A35)

Related Items (14)

Sharp quantitative stability for isoperimetric inequalities with homogeneous weights ⋮ Condenser capacity and hyperbolic perimeter ⋮ A minimal partition problem with trace constraint in the Grushin plane ⋮ Symmetry and isoperimetry for Riemannian surfaces ⋮ Quantitative isoperimetric inequalities in \(\mathbb H^n\) ⋮ Contraction property of certain classes of log-\(\mathcal{M}\)-subharmonic functions in the unit ball ⋮ The sharp Sobolev type inequalities in the Lorentz-Sobolev spaces in the hyperbolic spaces ⋮ Stability of the isodiametric problem on the sphere and in the hyperbolic space ⋮ The Riemannian quantitative isoperimetric inequality ⋮ A Heintze-Karcher type inequality in hyperbolic space ⋮ Sharp Adams-Moser-Trudinger type inequalities in the hyperbolic space ⋮ A note on strong-form stability for the Sobolev inequality ⋮ A Strong Form of the Quantitative Wulff Inequality ⋮ Quantitative stability for minimizing Yamabe metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Minimality via second variation for a nonlocal isoperimetric problem
• Regularity of sets with quasiminimal boundary surfaces in metric spaces
• A mass transportation approach to quantitative isoperimetric inequalities
• On asymmetry and capacity
• Quasiminimal surfaces of codimension 1 and John domains
• Sharp stability inequalities for planar double bubbles
• A selection principle for the sharp quantitative isoperimetric inequality
• Isoperimetry and stability properties of balls with respect to nonlocal energies
• A sharp quantitative isoperimetric inequality in higher codimension
• A quantitative isoperimetric inequality on the sphere
• Stability of the Steiner symmetrization of convex sets
• The sharp quantitative isoperimetric inequality
• A strong form of the quantitative isoperimetric inequality
• Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl
• Sets of Finite Perimeter and Geometric Variational Problems
• On the isoperimetric deficit in Gauss space
• A quantitative isoperimetric inequality in n-dimensional space.
• A strong minimax property of nondegenerate minimal submanifolds.
• Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals
• Stability in the Isoperimetric Problem for Convex or Nearly Spherical Domains in R n

This page was built for publication: A sharp quantitative isoperimetric inequality in hyperbolic \(n\)-space