Results 21 to 30 of about 448 (58)
Differentiability, Porosity and Doubling in Metric Measure Spaces [PDF]
Proc. Amer. Math. Soc. 141 (2013), pp. 971-985, 2011 We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show if we only require an approximate differentiable structure the measure need no longer be pointwise doubling.
arxiv +1 more source
, 2012 We give an intrinsic characterization of all subsets of a doubling metric space that can arise as a member of some system of dyadic cubes on the underlying space, as constructed by M.
Hytönen, Tuomas, Kairema, Anna
core +1 more source
Shape optimization problems on metric measure spaces [PDF]
, 2013 We consider shape optimization problems of the form $$\min\big\{J(\Omega)\ :\ \Omega\subset X,\ m(\Omega)\le c\big\},$$ where $X$ is a metric measure space and $J$ is a suitable shape functional.
Buttazzo, Giuseppe, Velichkov, Bozhidar
core +2 more sources
Capacitary density and removable sets for Newton-Sobolev functions in metric spaces [PDF]
arXiv, 2022 In a complete metric space equipped with a doubling measure and supporting a $(1,1)$-Poincar\'e inequality, we show that every set satisfying a suitable capacitary density condition is removable for Newton-Sobolev functions.
arxiv
Trace and density results on regular trees [PDF]
, 2019 We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.
arxiv +1 more source
A note on rearrangement Poincaré inequalities and the doubling condition [PDF]
arXiv, 2023 We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.
arxiv
Lusin-type theorems for Cheeger derivatives on metric measure spaces
, 2015 A theorem of Lusin states that every Borel function on $R$ is equal almost everywhere to the derivative of a continuous function. This result was later generalized to $R^n$ in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of
David, Guy C.
core +2 more sources
Approximation by uniform domains in doubling quasiconvex metric spaces [PDF]
arXiv, 2020 We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
arxiv
Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices
, 2012 Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated.
Malý, Lukáš
core +1 more source
Quasihyperbolic Metric Universal Covers [PDF]
arXiv, 2020 We present a simple analytical proof that the natural metric universal cover of a quasihyperbolic planar domain is a complete Hadamard metric space.
arxiv