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math.MG2019★ 19 cited
Linear bounds for constants in Gromov's systolic inequality and related results
Alexander Nabutovsky
Let be a closed Riemannian manifold. Larry Guth proved that there exists with the following property: if for some the volume of each metric ball of radius is…
math.DG2019
Filling metric spaces
Yevgeny Liokumovich, Boris Lishak, Alexander Nabutovsky +1
We prove a new version of isoperimetric inequality: Given a positive real , a Banach space , a closed subset of metric space and a continuous map …
math.MG2019
Geodesic Nets: Some Examples and Open Problems
Alexander Nabutovsky, Fabian Parsch
Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general propertie…