Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
نویسندگان
چکیده
منابع مشابه
Diameter-volume Inequalities and Isoperimetric Filling Problems in Metric Spaces
In this article we study metric spaces which admit polynomial diameter-volume inequalities for k-dimensional cycles. These generalize the notion of cone type inequalities introduced by M. Gromov in his seminal paper Filling Riemannian manifolds. In a first part we prove a polynomial isoperimetric inequality for k-cycles in such spaces, generalizing Gromov’s isoperimetric inequality of Euclidean...
متن کاملSharp and Rigid Isoperimetric Inequalities in Metric-measure Spaces with Lower Ricci Curvature Bounds
We prove that if (X, d,m) is a metric measure space with m(X) = 1 having (in a synthetic sense) Ricci curvature bounded from below by K > 0 and dimension bounded above by N ∈ [1,∞), then the classic Lévy-Gromov isoperimetric inequality (together with the recent sharpening counterparts proved in the smooth setting by E. Milman for any K ∈ R, N ≥ 1 and upper diameter bounds) hold, i.e. the isoper...
متن کاملIsoperimetric Inequalities of Euclidean Type in Metric Spaces
1.1. Statement of the main result. The isoperimetric problem of euclidean type for a space X and given classes Ik−1, Ik, and Ik+1 of surfaces of dimension k − 1, k, and k + 1 in X , together with boundary operators Ik+1 ∂ −→ Ik ∂ −→ Ik−1 and a volume function M on each class, asks the following: Does there exist for every surface T ∈ Ik without boundary, ∂T = 0, a surface S ∈ Ik+1 with ∂S = T a...
متن کاملIsoperimetric 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 کاملGeneralized isoperimetric inequalities.
A new class of isoperimetric inequalities is described and illustrated.
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: Journal of Functional Analysis
سال: 2016
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2016.02.016