Results 41 to 50 of about 448 (58)

Comparisons of relative BV-capacities and Sobolev capacity in metric spaces [PDF]

, 2011
We study relations between the variational Sobolev 1-capacity and versions of variational BV-capacity in a complete metric space equipped with a doubling measure and supporting a weak $(1,1)$-Poincar\'e inequality.
Hakkarainen, Heikki, Shanmugalingam, Nageswari   +1 more
core  

Vector-valued non-homogeneous Tb theorem on metric measure spaces [PDF]

Rev. Mat. Iberoamericana 28 (4) (2012) 961-998, 2010
We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is quite general with respect to both of them.
arxiv  

Cheeger's differentiation theorem via the multilinear Kakeya inequality

, 2019
Suppose that $(X,d,\mu)$ is a metric measure space of finite Hausdorff dimension and that, for every Lipschitz $f \colon X \to \mathbb R$, $\operatorname{Lip}(f,\cdot)$ is dominated by every upper gradient of $f$.
Bate, David, Kangasniemi, Ilmari, Orponen, Tuomas   +2 more
core  

Global higher integrability for parabolic quasiminimizers in metric spaces [PDF]

arXiv, 2013
We prove higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces, related to the heat equation. We assume the underlying metric measure space to be equipped with a doubling measure and to support a weak Poincar\'e-inequality.
arxiv  

Homology by metric currents [PDF]

arXiv, 2013
Metric currents are, in a certain sense, a metric analogous of flat currents, therefore are related to the geometry of the space and of their support. In this short note, we try to give some evidence for the previous statement, by showing that the homology which can be defined by means of metric normal currents coincides, on nice enough metric spaces ...
arxiv  

Besicovitch type properties in metric spaces

, 2019
We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, with emphasis on geometrically doubling spaces.Comment: 14 ...
Aldaz, J. M.
core  

A notion of fine continuity for BV functions on metric spaces [PDF]

arXiv, 2015
In the setting of a metric space equipped with a doubling measure supporting a Poincar\'e inequality, we show that BV functions are, in the sense of multiple limits, continuous with respect to a 1-fine topology, at almost every point with respect to the codimension 1 Hausdorff measure.
arxiv  

A Federer-style characterization of sets of finite perimeter on metric spaces [PDF]

arXiv, 2016
In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that a set $E$ is of finite perimeter if and only if $\mathcal H(\partial^1 I_E)<\infty$, that is, if and only if the codimension one Hausdorff measure of the \emph{$1$-fine boundary} of the set's measure theoretic interior $I_E$ is finite.
arxiv  

Quasihyperbolic geodesics are hyperbolic quasi-geodesics [PDF]

arXiv, 2017
This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hyperbolic and quasihyperbolic quasi-geodesics are the same curves.
arxiv  

Maximal function estimates and self-improvement results for Poincaré inequalities [PDF]

arXiv, 2017
Our main result is an estimate for a sharp maximal function, which implies a Keith-Zhong type self-improvement property of Poincar\'e inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.
arxiv