Additive colourful Carath\'eodory type results with an application to radii
Matthias Brugger, Maximilian Fiedler, Bernardo Gonz\'alez Merino, and Anja Kirschbaum
TL;DR
This paper investigates how the circumradius behaves under Minkowski addition in generalized Minkowski spaces, providing additive colourful Carathéodory type results under specific equilibrium conditions.
Contribution
It introduces new additive colourful Carathéodory type theorems related to circumradius in Minkowski spaces, expanding understanding of geometric properties under Minkowski addition.
Findings
Circumradius behavior characterized under Minkowski addition
Additive colourful Carathéodory results established
Applications to radii in generalized Minkowski spaces
Abstract
In this paper we study the behavior of the circumradius with respect to the Minkowski addition in generalized Minkowski spaces. To do so, we solve additive colourful Carath\'eodory type results, under certain equilibria conditions.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations