Dimensions, Whitney covers, and tubular neighborhoods

By A. Kaenmaki, Juha Lehrback, Matti Vuorinen. 2012

99 citations recorded by the source corpus.

Working in doubling metric spaces, we examine the connections between different dimensions, Whitney covers, and geometrical properties of tubular neighborhoods. In the Euclidean space, we relate these concepts to the behavior of the surface area of the boundaries of parallel sets. In particular, we give characterizations for the Minkowski and the spherical dimensions by means of the Whitney ball count.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f4f6c6b918dd58609d788b72d20156566b921f97

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Antti V. Vahakangas
2. L. Ihnatsyeva
3. Bartłomiej Dyda
4. Heli Tuominen
5. Juha Lehrbäck
6. Yuan Zhou
7. Rupert L. Frank
8. Jonathan M. Fraser

In Computational Mechanics

1. Heli Tuominen

In Mathematical Physics

1. Heli Tuominen
2. L. Ihnatsyeva
3. Bartłomiej Dyda

Citations in the corpus

• Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy–Sobolev -type Inequalities (2017, background): “, the lower Assouad dimension and the upper Assouad codimension; see [21].”