102 citations · 248 across the 18 of their papers we have counts for
19 papers
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…
General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem II
Richard J. Gardner, Daniel Hug, Sudan Xing +1
The general dual volume $\dveV(K)$ and the general dual Orlicz curvature measure $\deV(K, \cdot)$ were recently introduced for functions $G: (0, \infty)\times \sphere\rightarrow (0…
General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I
Richard J. Gardner, Daniel Hug, Wolfgang Weil +2
The general volume of a star body, a notion that includes the usual volume, the th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding ne…