S. Avvakumov

activity

20122023

most citedAny cyclic quadrilateral can be inscribed in any closed convex smooth curve

18 citations · 63 across the 14 of their papers we have counts for

collaborators

17 papers

math.MG2023

Boxing inequalities in Banach spaces and Riemannian manifolds

Sergey Avvakumov, Alexander Nabutovsky

We prove the following result: For each closed $n$ -dimensional manifold $M$ in a (finite or infinite-dimensional) Banach space $B$ , and each positive real $m \leq n$ there exists a…

math.AT2021

Topological lower bounds on the sizes of simplicial complexes and simplicial sets

Sergey Avvakumov, Roman Karasev

We prove that if an $n$ -dimensional space $X$ satisfies certain topological conditions then any triangulation of $X$ as well as any its representation as a simplicial set with cont…

math.MG2021

Systolic inequalities for the number of vertices

Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard +1

Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in…

math.MG2020

Equipartition of a segment

Sergey Avvakumov, Roman Karasev

We prove that, for any positive integer $m$ , a segment may be partitioned into $m$ possibly degenerate or empty segments with equal values of a continuous function $f$ of a segment…

math.CO2020

A subexponential size triangulation of $R P^{n}$

Karim Adiprasito, Sergey Avvakumov, Roman Karasev

We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a tr…

math.GT2019

Vanishing of all equivariant obstructions and the mapping degree

Sergey Avvakumov, Sergey Kudrya

Suppose that $n \neq = p^{k}$ and $n \neq = 2 p^{k}$ for all $k$ and all primes $p$ . We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $S_{n}$ th…

cs.CG2019

Homotopic curve shortening and the affine curve-shortening flow

Sergey Avvakumov, Gabriel Nivasch

We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call "homotopic curve shortening" (HCS), starts…

math.GT2019★ 1 cited

Stronger counterexamples to the topological Tverberg conjecture

S. Avvakumov, R. Karasev, A. Skopenkov

Denote by $Δ_{M}$ the $M$ -dimensional simplex. A map $f : Δ_{M} \to R^{d}$ is an almost $r$ -embedding if $f σ_{1} \cap \dots \cap f σ_{r} = \emptyset$ whenever $σ_{1}, \dots, σ_{r}$ are pairw…

math.AT2019★ 11 cited

Envy-free division using mapping degree

Sergey Avvakumov, Roman Karasev

In this paper we study envy-free division problems. The classical approach to such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and f…

math.CO2018★ 1 cited

A Note on a Picture-Hanging Puzzle

Radoslav Fulek, Sergey Avvakumov

In the picture-hanging puzzle we are to hang a picture so that the string loops around $n$ nails and the removal of any nail results in a fall of the picture. We show that the leng…

math.MG2018★ 7 cited

Convex fair partitions into an arbitrary number of pieces

Arseniy Akopyan, Sergey Avvakumov, Roman Karasev

We prove that any convex body in the plane can be partitioned into $m$ convex parts of equal areas and perimeters for any integer $m \geq 2$ ; this result was previously known for pri…

math.MG2017★ 18 cited

Any cyclic quadrilateral can be inscribed in any closed convex smooth curve

Arseniy Akopyan, Sergey Avvakumov

We prove that any cyclic quadrilateral can be inscribed in any closed convex $C^{1}$ -curve. The smoothness condition is not required if the quadrilateral is a rectangle.

math.GT2017

The classification of linked $3$ -manifolds in $6$ -space

Sergey Avvakumov

Let $M_{1}$ and $M_{2}$ be closed connected orientable $3$ -manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_{1} ⊔ M_{2} \to S^{6}$ .

math.GT2015★ 10 cited

Eliminating Higher-Multiplicity Intersections, III. Codimension 2

S. Avvakumov, I. Mabillard, A. Skopenkov +1

We study conditions under which a finite simplicial complex $K$ can be mapped to $R^{d}$ without higher-multiplicity intersections. An almost $r$ -embedding is a map $f: K\to…

math.GT2014

The classification of certain linked $3$ -manifolds in $6$ -space

Sergey Avvakumov

We work entirely in the smooth category. An embedding $f : (S^{2} \times S^{1}) ⊔ S^{3} \to R^{6}$ is {\it Brunnian}, if the restriction of $f$ to each component is isoto…

math-ph2013★ 14 cited

Euler elasticae in the plane and the Whitney--Graustein theorem

Sergey Avvakumov, Oleg Karpenkov, Alexey Sossinsky

In this paper, we apply classical energy principles to Euler elasticae, i.e., closed C^2 curves in the plane supplied with the Euler functional U (the integral of the square of the…

math.GT2012★ 1 cited

How do curved spheres intersect in 3-space?

Sergey Avvakumov

The following problem was proposed in 2010 by S. Lando. Let $M$ and $N$ be two unions of the same number of disjoint circles in a sphere. Do there always exist two spheres in 3-spa…

Boxing inequalities in Banach spaces and Riemannian manifolds

Topological lower bounds on the sizes of simplicial complexes and simplicial sets

Systolic inequalities for the number of vertices

Equipartition of a segment

A subexponential size triangulation of RPn

Vanishing of all equivariant obstructions and the mapping degree

Homotopic curve shortening and the affine curve-shortening flow

Stronger counterexamples to the topological Tverberg conjecture

Envy-free division using mapping degree

A Note on a Picture-Hanging Puzzle

Convex fair partitions into an arbitrary number of pieces

Any cyclic quadrilateral can be inscribed in any closed convex smooth curve

The classification of linked 3-manifolds in 6-space

Eliminating Higher-Multiplicity Intersections, III. Codimension 2

The classification of certain linked 3-manifolds in 6-space

Euler elasticae in the plane and the Whitney--Graustein theorem

How do curved spheres intersect in 3-space?

A subexponential size triangulation of $R P^{n}$

The classification of linked $3$ -manifolds in $6$ -space

The classification of certain linked $3$ -manifolds in $6$ -space