Displaying similar documents to “Randomness and pattern in convex geometric analysis.”

The skeleta of convex bodies

David G. Larman (2009)

Banach Center Publications

Similarity:

The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.

Zonoids with an equatorial characterization

Rafik Aramyan (2016)

Applications of Mathematics

Similarity:

It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is...

Essentially-Euclidean convex bodies

Alexander E. Litvak, Vitali D. Milman, Nicole Tomczak-Jaegermann (2010)

Studia Mathematica

Similarity:

In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]-dimensional subspace which has further proportional-dimensional Euclidean subspaces of any proportion. We consider a space X₁ = (ℝⁿ,||·||₁) with the property that if a space X₂ = (ℝⁿ,||·||₂) is "not too far" from X₁ then there exists a [λn]-dimensional subspace E⊂ ℝⁿ such that E₁ = (E,||·||₁)...