Browsing School of Mathematics Faculty Publications by Subject "Isoperimetry"
Now showing items 15 of 5

A Characterization of Gaussian Measures via the Isoperimetric Property of HalfSpaces
(Georgia Institute of Technology, 19950725)If the halfspaces of the form {x\in R^n: x_1 \le c} are extremal in the isoperimetric problem for the product measure \mu^n, n\ge 2, then \mu is Gaussian. 
Dimension Free Weak Concentration of Measure Phenomenon
(Georgia Institute of Technology, 19950724)For product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form \mu^n (A + h[1,1]^n)\ge R_h(\mu^n(A)) to hold; for a ... 
Isoperimetric Constants for Product Probability Measures
(Georgia Institute of Technology, 19950724)A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived. 
Sharp Constants in Some Multiplicative Sobolev Inequalities
(Georgia Institute of Technology, 19950916)The optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities ... 
Variance of Lipschitz Functions and an Isoperimetric Problem for a Class of Product Measures
(Georgia Institute of Technology, 19950710)The maximal variance of Lipschitz functions (with respect to the \ell_1distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability ...