CONFORMAL DIMENSION OF THE BROWNIAN GRAPH

被引：0

作者：

Binder, Ilia ^{[1
]}

Hakobyan, Hrant ^{[2
]}

Li, Wen-Bo ^{[3
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON, Canada

[2] Kansas State Univ, Dept Math, Manhattan, KS USA

[3] Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China

来源：

DUKE MATHEMATICAL JOURNAL | 2025年 / 174卷 / 07期

基金：

加拿大自然科学与工程研究理事会;

关键词：

HAUSDORFF DIMENSION; ASSOUAD DIMENSION; SETS;

D O I：

10.1215/00127094-2024-0059

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Conformal dimension of a metric space X, denoted by dims X, is the infimum of the Hausdorff dimension among all its quasisymmetric images. If conformal dimension of X is equal to its Hausdorff dimension, X is said to be minimal for conformal dimension. In this paper we show that the graph of 1-dimensional Brownian motion is almost surely minimal for conformal dimension. We also give other examples of sets that are minimal for conformal dimension. These include Bedford-McMullen self-affine carpets with uniform fibers as well as graphs of continuous functions of Hausdorff dimension d, for every d 2 [1, 2]. The main technique in the proofs is the construction of "rich families of minimal sets of conformal dimension 1." The latter concept is quantified using Fuglede's modulus of measures.

引用

页码：1341 / 1405

页数：65

共 50 条

[1] Hausdorff dimension of the SLE curve intersected with the real line [J].