Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On the Density Problem in the Parabolic Space
View through CrossRef
In this work we establish relationships between densities, tangents, and rectifiability in parabolic spaces, namely
R
n
+
1
\mathbb {R}^{n+1}
equipped with parabolic dilations. In particular, we prove a Marstrand-Mattila rectifiability criterion for measures of general dimension, we provide a characterisation through densities of intrinsic rectifiable measures, and we study the structure of
1
1
-codimensional uniform measures. Finally, we apply some of our results to the study of a quantitative version of parabolic rectifiability: we prove that the weak constant density condition for a
1
1
-codimensional Ahlfors-regular measure implies the bilateral weak geometric lemma.
American Mathematical Society (AMS)
Title: On the Density Problem in the Parabolic Space
Description:
In this work we establish relationships between densities, tangents, and rectifiability in parabolic spaces, namely
R
n
+
1
\mathbb {R}^{n+1}
equipped with parabolic dilations.
In particular, we prove a Marstrand-Mattila rectifiability criterion for measures of general dimension, we provide a characterisation through densities of intrinsic rectifiable measures, and we study the structure of
1
1
-codimensional uniform measures.
Finally, we apply some of our results to the study of a quantitative version of parabolic rectifiability: we prove that the weak constant density condition for a
1
1
-codimensional Ahlfors-regular measure implies the bilateral weak geometric lemma.
Related Results
Linking White‐Tailed Deer Density, Nutrition, and Vegetation in a Stochastic Environment
Linking White‐Tailed Deer Density, Nutrition, and Vegetation in a Stochastic Environment
ABSTRACT
Density‐dependent behavior underpins white‐tailed deer (
Odocoileus virginianus
) theory and...
Parabolic quantitative rectifiability
Parabolic quantitative rectifiability
The purpose of this thesis is to develop a parabolic analog of uniform rectifiability. First, we provide a very general result concerning corona decompositions and the big pieces f...
Seditious Spaces
Seditious Spaces
The title ‘Seditious Spaces’ is derived from one aspect of Britain’s colonial legacy in Malaysia (formerly Malaya): the Sedition Act 1948. While colonial rule may seem like it was ...
Approximation of Parabolic Fuzzy Numbers
Approximation of Parabolic Fuzzy Numbers
Most of the real world problems are complex that is raised from uncertainity in the form of ambiguity. To overcome the ambiguity and impreciseness, Zadeh [20] introduced fuzzy set ...
Depth and Diameter's Effect on Rim Angle of Solar Parabolic Dish Collector
Depth and Diameter's Effect on Rim Angle of Solar Parabolic Dish Collector
Abstract: Energy exists in numerous forms, which include heat, light, and radiation. We aim to optimise solar radiation at low, moderate, and high temperatures. Concentrating colle...
Fundamental Concepts and Methodology for the Analysis of Animal Population Dynamics, with Particular Reference to Univoltine Species
Fundamental Concepts and Methodology for the Analysis of Animal Population Dynamics, with Particular Reference to Univoltine Species
This paper presents some concepts and methodology essential for the analysis of population dynamics of univoltine species. Simple stochastic difference equations, comprised of endo...
Notes on BLO spaces with parabolic structure
Notes on BLO spaces with parabolic structure
For the natural parabolic maximal operators $\mathfrak M^{\pm}_{\gamma}$ with time lag $\gamma\in(0,1)$, the author first establishes its boundedness from parabolic $\mathrm{BMO}$ ...
Shape Comparison for Solar Thermal Parabolic Collector
Shape Comparison for Solar Thermal Parabolic Collector
The KU EcoHawks are a mechanical engineering, undergraduate, senior design group at the University of Kansas that focuses on projects emphasizing a sustainable approach to automobi...