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14 papers · 1 filter
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…
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…
The Dual Orlicz-Brunn-Minkowski Theory
Richard J. Gardner, Daniel Hug, Wolfgang Weil +1
This paper introduces the dual Orlicz-Brunn-Minkowski theory for star sets. A radial Orlicz addition of two or more star sets is proposed and a corresponding dual Orlicz-Brunn-Mink…