24 citations · 63 across the 13 of their papers we have counts for
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Boxing inequalities in Banach spaces and Riemannian manifolds
Sergey Avvakumov, Alexander Nabutovsky
We prove the following result: For each closed -dimensional manifold in a (finite or infinite-dimensional) Banach space , and each positive real there exists a…
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…
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…
Complexity of Unknotting of Trivial 2-knots
Boris Lishak, Alexander Nabutovsky
We construct families of trivial -knots in such that the maximal complexity of -knots in any isotopy connecting with the standard unknot grows fast…
Balanced presentations of the trivial group and four-dimensional geometry
Boris Lishak, Alexander Nabutovsky
We prove that 1) There exist infinitely many non-trivial codimension one "thick" knots in ; 2) For each closed four-dimensional smooth manifold and for each suffi…