122 citations · 134 across the 4 of their papers we have counts for
7 papers
Affine vs. Euclidean isoperimetric inequalities
Christoph Haberl, Franz E. Schuster
It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly implies the classical…
Centro-Affine Tensor Valuations
Christoph Haberl, Lukas Parapatits
We completely classify all measurable -covariant symmetric tensor valuations on convex polytopes containing the origin in their interiors. It is shown that es…
Moments and Valuations
Christoph Haberl, Lukas Parapatits
All measurable and -covariant vector valued valuations on convex polytopes containing the origin in their interiors are completely classified. The moment vect…
Valuations and Surface Area Measures
Christoph Haberl, Lukas Parapatits
We consider valuations defined on polytopes containing the origin which have measures on the sphere as values. We show that the classical surface area measure is essentially the on…
The Centro-Affine Hadwiger Theorem
Christoph Haberl, Lukas Parapatits
All upper semicontinuous and SL(n) invariant valuations on convex bodies containing the origin in their interiors are completely classified. Each such valuation is shown to be a li…
An Asymmetric Affine Pólya--Szegö Principle
Christoph Haberl, Franz E. Schuster, Jie Xiao
An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya--Szegö symmetrization principle for functions on .…