Results 21 to 30 of about 85 (68)

LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS

Forum of Mathematics, Sigma, 2015
We investigate the interplay between the local and asymptotic geometry of a set $A\subseteq \mathbb{R}^{n}$ and the geometry of model sets ${\mathcal{S}}\subset {\mathcal{P}}(\mathbb{R}^{n})$, which approximate $A$ locally uniformly on small scales.
MATTHEW BADGER, STEPHEN LEWIS
doaj   +1 more source

A Generalization of the Real Mean Value Inequality

, 2005
In dieser Arbeit wird eine Mittelwertungleichung für banachraumwertige Funktionen auf einem kompakten Intervall vorgestellt. Im Spezialfall reellwertiger Funktionen wurde diese Mittelwertungleichung bereits von Dale E.
Rosenberger, B. (Burkard)
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Konstruktion eines äußeren Längenmaßes auf Banachräumen

, 2005
Zur Längenmessung in R bedient man sich des äußeren Lebesgue-Maßes. Möchte man dieses Konzept der Längenmessung auf einen beliebigen Banachraum übertragen, so ergeben sich begriffliche Schwierigkeiten, denn intuitiv ist zunächst unklar, was man unter der
Rosenberger, B. (Burkard)
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Qualitative Lipschitz to bi-Lipschitz decomposition

Analysis and Geometry in Metric Spaces
We prove that any Lipschitz map that satisfies a condition inspired by the work of G. David may be decomposed into countably many bi-Lipschitz pieces.
Bate David
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A note on the diameter of small sub-Riemannian balls

Analysis and Geometry in Metric Spaces
We observe that the diameter of small (in a locally uniform sense) balls in C 1,1 sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to C 0, the diameter is arbitrarily close to ...
Di Marco Marco, Somma Gianluca, Vittone Davide   +2 more
doaj   +1 more source

Capacity and perimeter from logarithmic fractional Sobolev spaces on Carnot groups

Advances in Nonlinear Analysis
In this paper, we introduce the logarithmic fractional Sobolev space on Carnot groups and investigate the various functional-geometric aspects of the corresponding functional capacity.
Zhao Nan, Liu Yu
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Uniform convergence of adversarially robust classifiers

European Journal of Applied Mathematics
In recent years, there has been significant interest in the effect of different types of adversarial perturbations in data classification problems. Many of these models incorporate the adversarial power, which is an important parameter with an associated
Rachel Morris, Ryan Murray
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C1,α-rectifiability in low codimension in Heisenberg groups

Analysis and Geometry in Metric Spaces
A natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability ...
Idu Kennedy Obinna, Maiale Francesco Paolo   +1 more
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Isoperimetric problems and lower bounds on curvature

Analysis and Geometry in Metric Spaces
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry (Granada, July ...
Antonelli Gioacchino
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Topological minimal sets and their applications

, 2011
In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets.
Xiangyu Liang
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