arXiv subjects

Artur Tursunbaev

Publications and source records attributed to Artur Tursunbaev.

2 recordsLinked to original sources

arXiv2026

Subgroups of free groups with the same derived subgroup

We prove that if H and K are subgroups of a free group F of arbitrary rank and $H'=K'\ne 1$, then $H=K$. As a consequence, if R is a noncyclic subgroup of a free group F and $R'$ is normal in F, then R is normal in F. This gives a positive answer to a problem of Shpilrain, originally posed as Problem 11.124 in the Kourovka Notebook and later appearing as Problem F15 in Kapovich-Myasnikov-Shpilrain.

math.GR↗

arXiv2026

Truncations for fractional Laplacians

Let $Ω\subset\mathbb R^n$ be a bounded Lipschitz domain. We prove and widely generalize a conjecture of A.\,I.~Nazarov \cite{Naz21}: for $s\in(1,\frac 32)$ the quadratic form $Q^{\rm SP}_s[u]$ of the spectral fractional Dirichlet Laplacian strictly increases under the map $u\mapsto|u|$ provided $u\in\tilde H^s(Ω)$ changes sign in $Ω$.

math.AP↗