Quadratic metric comparisons
Nina Lebedeva, Anton Petrunin, Vladimir Zolotov
TL;DR
This paper investigates how quadratic inequalities influence the structure of length spaces by examining the relationships among distances in quadruples of points.
Contribution
It introduces a new framework for analyzing length spaces through quadratic metric comparisons, providing insights into their geometric properties.
Findings
Characterization of length spaces satisfying quadratic inequalities
Identification of geometric constraints imposed by quadratic metrics
Potential applications in metric geometry and related fields
Abstract
We study the effects on length spaces imposed by quadratic inequalities on the six distances between the points in every quadruple.
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Taxonomy
TopicsMathematics and Applications · Mathematical Inequalities and Applications · Analytic and geometric function theory