1 citations · 2 across the 6 of their papers we have counts for
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Length of a closed geodesic in 3-manifolds of positive scalar curvature
Yevgeny Liokumovich, Davi Maximo, Regina Rotman
Let be a closed -dimensional Riemannian manifold with positive scalar curvature, . We show that contains a non-trivial closed geodesic of length less than $2…
The Smale conjecture and min-max theory
Daniel Ketover, Yevgeny Liokumovich
We give a new proof of the Smale conjecture for and all lens spaces using minimal surfaces and min-max theory. For , the conjecture was first proved…
On the waist and width inequality in complete 3-manifolds with positive scalar curvature
Yevgeny Liokumovich, Zhichao Wang
We show that a complete non-compact 3-manifold with scalar curvature bounded below by a positive constant admits a singular foliation by surfaces of controlled area and diameter.
Geodesic nets on non-compact Riemannian manifolds
Gregory R. Chambers, Yevgeny Liokumovich, Alexander Nabutovsky +1
A geodesic flower is a finite collection of geodesic loops based at the same point that satisfy the following balancing condition: The sum of all unit tangent vectors to all ge…
Parametric inequalities and Weyl law for the volume spectrum
Larry Guth, Yevgeny Liokumovich
We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities:…
Generic density of geodesic nets
Yevgeny Liokumovich, Bruno Staffa
We prove that for a Baire-generic Riemannian metric on a closed smooth manifold, the union of the images of all stationary geodesic nets forms a dense set.