Capacity density of subanalytic sets in higher dimension
type: Item
instance of: scholarly article
title: Capacity density of subanalytic sets in higher dimension
zbMATH Open document ID: 1122.32005
author: Tobias Kaiser
published in: Potential Analysis
publication date: 2007-06-07T00:00:00Z
review text: This paper concerns the relationship between capacity and subanalytic geometry. Let \(B_{r}(x)\) denote the open ball of centre \(x\) and radius \(r\) in \(\mathbb{R}^{n}\) \((n\geq 3)\), and let \(c(\cdot )\) denote Newtonian capacity. The main result says that, if \(E\subset \mathbb{R}^{n}\) is a subanalytic set, then the capacity density \(\lim_{r\rightarrow 0}c(E\cap B_{r}(x))/c(B_{r}(x))\) exists at every point \(x\in \mathbb{R}^{n}\). The author [Ill. J. Math. 49, 719--736 (2005; Zbl 1092.31004)] had previously established the corresponding result for two dimensions, but the proof of the higher dimensional case required new ideas.
Mathematics Subject Classification ID: 32B20
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 5162167
zbMATH Keywords: subanalytic set
zbMATH Keywords: Newtonian capacity
reviewed by: Stephen J. Gardiner
MaRDI profile type: Publication
full work available at URL: s11118-007-9043-7
OpenAlex ID: W2057580439
cites work: Q4513495
cites work: Semianalytic and subanalytic sets
cites work: Real equisingularity: Lelong numbers and polar projections
cites work: Tame geometry with application in smooth analysis
cites work: Q4692700
cites work: Capacity in subanalytic geometry
cites work: Q4037361
cites work: Densité des ensembles sous-analytiques. (On the density of subanalytic sets)
cites work: Capacity and measure densities
cites work: Q4141474
cites work: Capacity and measure
cites work: The capacity density and the Hausdorff dimension of fractal sets
DOI: 10.1007/S11118-007-9043-7
description: scientific article; zbMATH DE number 5162167