Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A criterion for pure unrectifiability of sets (via universal vector bundle)

100%

Delladio S.

Annales Polonici Mathematici

2011

tom 102

nr 1

73-78

Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let $π_V$ denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an $𝓗 ^m$-measurable subset of ℝⁿ with $𝓗 ^m(A) < ∞$. Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle ${(V,v)| V ∈ G(n,m), v ∈ V}$ such that, for all P ∈ A, one has $𝓗 ^{m(n-m)}({V ∈ G(n,m)|(V,π_V(P)) ∈ Z}) > 0$. One can replace "for all P ∈ A" by "for $𝓗 ^m$-a.e. P ∈ A".

Slicing of generalized surfaces with curvature measures and diameter's estimate

100%

Delladio S.

Annales Polonici Mathematici

1996

tom 64

nr 3

267-283

We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Delladio S.

1 2011

1 1996

Wyniki wyszukiwania

A criterion for pure unrectifiability of sets (via universal vector bundle)

Slicing of generalized surfaces with curvature measures and diameter's estimate