Packing dimension and Ahlfors regularity of porous sets in metric spaces

Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki, Tapio Rajala, Sari Rogovin, Ville Suomala

Type: Article

Publication Date: 2009-06-05

Citations: 46

DOI: https://doi.org/10.1007/s00209-009-0555-2

View Publication

Download PDF

Locations

Mathematische Zeitschrift - View
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Dimensions and Porosities	2010	Esa Järvenpää
+	Hausdorff and Packing Measures	2024
+	Density theorems for Hausdorff and packing measures	1995	Pertti Mattila
+	The density theorem and Hausdorff inequality for packing measure in general metric spaces	1995	Colleen D. Cutler
+ PDF Chat	Packing measures on ultrametric spaces	1988	Hermann Haase
+	Porosity and dimension of sets and measures	2009	Tapio Rajala
+	Some Fine Properties of Sets of Finite Perimeter in Ahlfors Regular Metric Measure Spaces	2001	Luigi Ambrosio
+ PDF Chat	Hausdorff Dimension and mean porosity	1997	Pekka Koskela Steffen Rohde
+ PDF Chat	Packing dimension of mean porous measures	2009	D. Beliaev Esa Järvenpää Maarit Järvenpää Antti Käenmäki Tapio Rajala Stanislav Smirnov Ville Suomala
+	Hausdorff measures and packing premeasures	2004	薫秦野弘明連絡相川
+	Hausdorff measures and packing premeasures	2004	Kaoru Hatano Hiroaki Aikawa
+	Hausdorff dimension of Lebesgue sets for W α p classes on metric spaces	2007	Михаил Александрович Прохорович
+	Regularities of general Hausdorff and packing functions	2019	Zied Douzi Bilel Selmi
+	A Note on ᓂ-Porous Sets	1991	Zajíček
+	Descriptive properties related to porosity and density for compact sets on the real line	2007	Sz. Gła̧b
+ PDF Chat	Small non-σ-porous sets in topologically complete metric spaces	1998	Luděk Zajı́ček
+	Hausdorff, Similarity, and Packing Dimensions	2020	Eric Rosenberg
+	Weakly porous sets and Muckenhoupt $A_p$ distance functions	2022	Theresa C. Anderson Juha Lehrbäck Carlos Mudarra Antti V. Vähäkangas
+ PDF Chat	Comparing the Hausdorff and packing measures of sets of small dimension in metric spaces	2010	Tapio Rajala
+	Scaling properties of Hausdorff and packing measures	2001	Marianna Csörnyei R. Daniel Mauldin

Works That Cite This (45)

Action	Title	Year	Authors
+	Volume growth of quasihyperbolic balls	2012	Xiaohui Zhang Riku Klén Ville Suomala Матти Вуоринен
+	Minkowski dimension for measures	2022	K. J. Falconer Jonathan M. Fraser Antti Käenmäki
+ PDF Chat	Dynamics of the scenery flow and geometry of measures	2015	Antti Käenmäki Tuomas Sahlsten Pablo Shmerkin
+	Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces	2017	Eero Saksman Tomás Soto
+	Следы пространств Соболева на нерегулярных подмножествах метрических пространств с мерой	2023	Alexander Tyulenev
+	Quasiregular mappings to generalized manifolds	2009	Jani Onninen Kai Rajala
+	Hyperbolic type metrics and distortion of quasiconformal mappings	2013	Shouxin Zhang
+ PDF Chat	Рост объемов квазигиперболических шаров	2017	Xiaohui Zhang Riku Klén Ville Suomala Матти Вуоринен
+ PDF Chat	Porosities of Mandelbrot Percolation	2019	Artemi Berlinkov Esa Järvenpää
+	From optimal transportation to optimal teleportation	2016	Gershon Wolansky

Works Cited by This (24)

Action	Title	Year	Authors
+	The density theorem and Hausdorff inequality for packing measure in general metric spaces	1995	Colleen D. Cutler
+	Fractured fractals and broken dreams: self-similar geometry through metric and measure	1999	Guy David Stephen Semmes
+	Measure and integral	1977	Richard L. Wheeden Antoni Zygmund
+	Lectures on Analysis on Metric Spaces	2001	Juha Heinonen
+ PDF Chat	Every complete doubling metric space carries a doubling measure	1998	Jouni Luukkainen Eero Saksman
+ PDF Chat	Asymptotically sharp dimension estimates for $k$-porous sets	2005	Esa Järvenpää Maarit Järvenpää Antti Käenmäki Ville Suomala
+	Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability	1995	Pertti Mattila
+	Ahlfors-David regular sets and bilipschitz maps	2008	Pertti Mattila Pirjo Saaranen
+ PDF Chat	Porosity of Collet–Eckmann Julia sets	1998	Feliks Przytycki Steffen Rohde
+	Doubling conformal densities	2001	Mario Bonk Juha Heinonen Steffen Rohde