The Steiner Formula for Minkowski Valuations
Lukas Parapatits, Franz E. Schuster
TL;DR
This paper establishes a Steiner formula for Minkowski valuations and uses it to derive Brunn-Minkowski type inequalities, advancing the understanding of geometric valuations and their symmetries.
Contribution
It introduces a Steiner type formula for Minkowski valuations and applies it to obtain new inequalities, connecting valuation theory with geometric inequalities.
Findings
Steiner formula for Minkowski valuations established
New Brunn-Minkowski type inequalities derived
Connections between valuations and geometric inequalities shown
Abstract
A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations, this new Steiner type formula is used to obtain a family of Brunn-Minkowski type inequalities for rigid motion intertwining Minkowski valuations.
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Taxonomy
TopicsPoint processes and geometric inequalities · Probabilistic and Robust Engineering Design · Robotic Mechanisms and Dynamics