The rate of convergence of Steklov means on metric measure spaces and Hausdorff dimension

2011 ◽  
Vol 89 (1-2) ◽  
pp. 156-159 ◽  
Author(s):  
V. G. Krotov ◽  
M. A. Prokhorovich
Keyword(s):  
Hausdorff Dimension ◽  
Rate Of Convergence ◽  
Metric Measure Spaces ◽  
Measure Spaces

scholarly journals Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

2013 ◽  
Vol 1 ◽  
pp. 232-254 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Jeremy T. Tyson ◽  
Kevin Wildrick
Keyword(s):  
Hausdorff Dimension ◽  
Heisenberg Group ◽  
Metric Space ◽  
Metric Spaces ◽  
Higher Dimension ◽  
Metric Measure Spaces ◽  
Regular Mapping ◽  
Sobolev Mappings ◽  
Measure Spaces ◽  
Left And Right

Abstract We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

scholarly journals Characterization of Low Dimensional RCD*(K, N) Spaces

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Hausdorff Dimension ◽  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Metric Measure Spaces ◽  
One Dimensional ◽  
Curvature Bounds ◽  
Measure Spaces ◽  
Low Dimensional ◽  
Regular Sets

AbstractIn this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking, a converse to the Lévy-Gromov’s isoperimetric inequality and was previously only known for Ricci limit spaces) which might be also of independent interest.

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals A note on the extension of BV functions in metric measure spaces

2008 ◽  
Vol 340 (1) ◽  
pp. 197-208 ◽  
Author(s):  
Annalisa Baldi ◽  
Francescopaolo Montefalcone
Keyword(s):  
Metric Measure Spaces ◽  
Bv Functions ◽  
Measure Spaces

scholarly journals Discretization of integrals on compact metric measure spaces

2021 ◽  
Vol 381 ◽  
pp. 107602
Author(s):  
Martin D. Buhmann ◽  
Feng Dai ◽  
Yeli Niu
Keyword(s):  
Metric Measure Spaces ◽  
Measure Spaces
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