Results 51 to 60 of about 520,398 (211)
Equivalence of Some Affine Isoperimetric Inequalities
Journal of Inequalities and Applications, 2009 We establish the equivalence of some affine isoperimetric inequalities which include the -Petty projection inequality, the -Busemann-Petty centroid inequality, the "dual" -Petty projection inequality, and the "dual" -Busemann-Petty inequality.
Yu Wuyang
doaj
HNN extensions and embedding theorems for groups
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The Higman–Neumann–Neumann (HNN) paper of 1949 is a landmark of group theory in the 20th century. The proof of its main theorem covers less than a page and uses only pre‐existing technology, but the construction that it introduced, the HNN extension, quickly became one of the principal tools of combinatorial group theory, widely used to build ...
Martin R. Bridson +1 more
wiley +1 more source
An isoperimetric inequality involving conformal mapping
, 1977 An isoperimetric inequality due to L. Bieberbach is generalized to the case of weighted areas.
Andrew Acker
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An optimal relative isoperimetric inequality in concave cylindrical domains in
Journal of Inequalities and Applications, 2000 We prove an optimal relative isoperimetric inequality in concave cylindrical domains in , which generalizes the well-known two-dimensional relative isoperimetric inequality in a planar sector with angle greater than or equal to .
Kim Inho
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Geodesics in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2015 We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from ...
Hajłasz Piotr, Zimmerman Scott
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Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs
Communications on Pure and Applied Mathematics, Volume 79, Issue 4, Page 1012-1072, April 2026.Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
wiley +1 more source
A tropical isoperimetric inequality
, 2017 arXiv:1611.04148International audienceWe introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality.
Joswig, Michael +2 more
core +2 more sources
On the structure of subsets of the discrete cube with small edge boundary
Discrete Analysis, 2018 On the structure of subsets of the discrete cube with small edge boundary, Discrete Analysis 2018:9, 29 pp. An isoperimetric inequality is a statement that tells us how small the boundary of a set can be given the size of the set, for suitable notions ...
David Ellis +2 more
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Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
wiley +1 more source
Isoperimetric Inequality for Disconnected Regions [PDF]
, 2021 The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon.
Sanki, Bidyut, Vadnere, Arya
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