Yevgeny Liokumovich

activity

20112026

most citedClassifying sufficiently connected PSC manifolds in

4

and

5

dimensions

12 citations · 61 across the 21 of their papers we have counts for

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Showing 2014Show all

5 papers · 1 filter

math.DG2014

Optimal sweepouts of a Riemannian 2-sphere

Gregory R. Chambers, Yevgeny Liokumovich

Given a sweepout of a Riemannian 2-sphere which is composed of curves of length less than L, we construct a second sweepout composed of curves of length less than L which are eithe…

math.DG2014

Lengths of three simple periodic geodesics on a Riemannian $2$ -sphere

Yevgeny Liokumovich, Alexander Nabutovsky, Regina Rotman

Let $M$ be a Riemannian $2$ -sphere. A classical theorem of Lyusternik and Shnirelman asserts the existence of three distinct simple non-trivial periodic geodesics on $M$ . In this p…

math.DG2014★ 5 cited

Families of short cycles on Riemannian surfaces

Yevgeny Liokumovich

Let $M$ be a closed Riemannian surface of genus $g$ . We construct a family of 1-cycles on $M$ that represents a non-trivial element of the k'th homology group of the space of cycle…

math.DG2014

Width, Ricci curvature and minimal hypersurfaces

Parker Glynn-Adey, Yevgeny Liokumovich

Let $(M, g_{0})$ be a closed Riemannian manifold of dimension $n$ , for $3 \leq n \leq 7$ , and non-negative Ricci curvature. Let $g = ϕ^{2} g_{0}$ be a metric in the conformal class of $g_…

math.DG2014

Slicing a 2-sphere

Yevgeny Liokumovich

We show that for every complete Riemannian surface $M$ diffeomorphic to a sphere with $k \geq 0$ holes there exists a Morse function $f : M \to R$ , which is constant…

Optimal sweepouts of a Riemannian 2-sphere

Lengths of three simple periodic geodesics on a Riemannian 2-sphere

Families of short cycles on Riemannian surfaces

Width, Ricci curvature and minimal hypersurfaces

Slicing a 2-sphere

Lengths of three simple periodic geodesics on a Riemannian $2$ -sphere