ASYMPTOTIC CONES AND POLYNOMIAL ISOPERIMETRIC INEQUALITIES
نویسندگان
چکیده
منابع مشابه
Isoperimetric Inequalities and the Asymptotic Rank of Metric Spaces
In this article we study connections between the asymptotic rank of a metric space and higher-dimensional isoperimetric inequalities. We work in the class of metric spaces admitting cone type inequalities which, in particular, includes all Hadamard spaces, i. e. simply connected metric spaces of nonpositive curvature in the sense of Alexandrov. As was shown by Gromov, spaces with cone type ineq...
متن کاملIsoperimetric Regions in Cones
We consider cones C = 0 × Mn and prove that if the Ricci curvature of C is nonnegative, then geodesic balls about the vertex minimize perimeter for given volume. If strict inequality holds, then they are the only stable regions.
متن کاملIsoperimetric Inequalities and Eigenvalues
An upper bound is given on the minimum distance between i subsets of the same size of a regular graph in terms of the i-th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the i-th largest eigenvalue, for any integer i. Our bounds are shown to be asymptotically tight. A recent result by Quenell relating the diameter, the second eigenvalue, and the girth of a...
متن کاملLp AFFINE ISOPERIMETRIC INEQUALITIES
Affine isoperimetric inequalities compare functionals, associated with convex (or more general) bodies, whose ratios are invariant under GL(n)-transformations of the bodies. These isoperimetric inequalities are more powerful than their better-known relatives of a Euclidean flavor. To be a bit more specific, this article deals with inequalities for centroid and projection bodies. Centroid bodies...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology
سال: 1999
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(98)00032-9