Heat flow and quantitative differentiation

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http://hdl.handle.net/10138/307055

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Hytonen , T & Naor , A 2019 , ' Heat flow and quantitative differentiation ' , European Mathematical Society. Journal , vol. 21 , no. 11 , pp. 3415-3466 . https://doi.org/10.4171/JEMS/906

Title: Heat flow and quantitative differentiation
Author: Hytonen, Tuomas; Naor, Assaf
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019
Language: eng
Number of pages: 52
Belongs to series: European Mathematical Society. Journal
ISSN: 1435-9855
URI: http://hdl.handle.net/10138/307055
Abstract: For every Banach space (Y, parallel to . parallel to(Y)) that admits an equivalent uniformly convex norm we prove that there exists c = c(Y) is an element of(0, infinity) with the following property. Suppose that n is an element of N and that X is an n-dimensional normed space with unit ball B-X. Then for every 1-Lipschitz function f : B-X -> Y and for every epsilon is an element of(0, 1/2] there exists a radius r >= exp (1/epsilon(cn)), a point x is an element of B-X with x + r B-X subset of B-X, and an affine mapping Lambda : X -> Y such that parallel to f (y) - Lambda (y)parallel to(Y)
Subject: Quantitative differentiation
uniform convexity
Littlewood-Paley theory
heat semigroup
metric embeddings
COARSE DIFFERENTIATION
UNIFORMLY CONVEX
QUASI-ISOMETRIES
LIPSCHITZ FUNCTIONS
BANACH-SPACES
GEOMETRY
RIGIDITY
APPROXIMATION
INEQUALITIES
REGULARITY
111 Mathematics
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