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math.DG2024
Stability of reverse isoperimetric inequalities in the plane: area, Cheeger, and inradius
Kostiantyn Drach, Kateryna Tatarko
In this paper, we present sharp stability results for various reverse isoperimetric problems in . Specifically, we prove the stability of the reverse isoperimetric ine…
math.MG2024
Answers to questions of Grünbaum and Loewner
S. Myroshnychenko, K. Tatarko, V. Yaskin
We construct a convex body in , , with the property that there is exactly one hyperplane passing through , the centroid of , such that the…
math.MG2024
Stability of simplex slicing
Serhii Myroshnychenko, Colin Tang, Kateryna Tatarko +1
We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary (not…