47 citations · 94 across the 10 of their papers we have counts for
11 papers
Approximation of rearrangements by polarizations
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
The symmetric decreasing rearrangement of functions on features in several seminal inequalities, such as the Pólya-Szegő inequality. The latter was shown by the auth…
Anisotropic symmetrization, convex bodies, and isoperimetric inequalities
Gabriele Bianchi, Andrea Cianchi, Paolo Gronchi
This work is concerned with a Pólya-Szegö type inequality for anisotropic functionals of Sobolev functions. The relevant inequality entails a double-symmetrization involving both t…
The Pólya-Szegő inequality for smoothing rearrangements
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
A basic version of the Pólya-Szegő inequality states that if is a Young function, the -Dirichlet energy -- the integral of -- of a suitable function $f\in…
Full rotational symmetry from reflections or rotational symmetries in finitely many subspaces
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi
Two related questions are discussed. The first is when reflection symmetry in a finite set of -dimensional subspaces, , implies full rotational symmetry, i…
Rearrangement and polarization
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi +1
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on . Rearrangements are map…
Convergence of symmetrization processes
Gabriele Bianchi, Richard J. Gardner, Paolo Gronchi
Steiner and Schwarz symmetrizations, and their most important relatives, the Minkowski, Minkowski-Blaschke, fiber, inner rotational, and outer rotational symmetrizations, are inves…
On the reverse Loomis-Whitney inequality
Stefano Campi, Peter Gritzmann, Paolo Gronchi
The present paper deals with the problem of computing (or at least estimating) the LW-number , i.e., the supremum of all such that for each convex body in $\mathbb{R}…
Symmetrization in Geometry
G. Bianchi, R. J. Gardner, P. Gronchi
The concept of an -symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i…
Reverse and dual Loomis-Whitney-type inequalities
Stefano Campi, Richard J. Gardner, Paolo Gronchi
Various results are proved giving lower bounds for the th intrinsic volume , , of a compact convex set in , in terms of the th intr…
Convergence in shape of Steiner symmetrizations
Gabriele Bianchi, Almut Burchard, Paolo Gronchi +1
There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examp…
Determining a rotation of a tetrahedron from a projection
Richard J. Gardner, Paolo Gronchi, Thorsten Theobald
The following problem, arising from medical imaging, is addressed: Suppose that is a known tetrahedron in with centroid at the origin. Also known is the orthogonal proje…