Zobrazeno 1 - 10
of 186
pro vyhledávání: '"Liokumovich P"'
We investigate the question: if an AI agent is known to be safe in one setting, is it also safe in a new setting similar to the first? This is a core question of AI alignment--we train and test models in a certain environment, but deploy them in anot
Externí odkaz:
http://arxiv.org/abs/2401.03529
Autor:
Ketover, Daniel, Liokumovich, Yevgeny
We give a new proof of the Smale conjecture for $\mathbb{RP}^3$ and all lens spaces using minimal surfaces and min-max theory. For $\mathbb{RP}^3$, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.
Comment: Updated vers
Comment: Updated vers
Externí odkaz:
http://arxiv.org/abs/2310.05756
Autor:
Liokumovich, Yevgeny, Wang, Zhichao
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.
Comment: 19 pages; 3 figures; comments are welcome!
Comment: 19 pages; 3 figures; comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2308.04044
A geodesic flower is a finite collection of geodesic loops based at the same point $p$ that satisfy the following balancing condition: The sum of all unit tangent vectors to all geodesic arcs meeting at $p$ is equal to the zero vector. In particular,
Externí odkaz:
http://arxiv.org/abs/2205.09242
Autor:
Guth, Larry, Liokumovich, Yevgeny
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: isoperimetric inequality and coarea inequality. We prove two such gene
Externí odkaz:
http://arxiv.org/abs/2202.11805
Autor:
Liokumovich, Yevgeny, Staffa, Bruno
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.
Externí odkaz:
http://arxiv.org/abs/2107.12340
Publikováno v:
Geom. Topol. 27 (2023) 1635-1655
We show that if $N$ is a closed manifold of dimension $n=4$ (resp. $n=5$) with $\pi_2(N) = 0$ (resp. $\pi_2(N)=\pi_3(N)=0$) that admits a metric of positive scalar curvature, then a finite cover $\hat N$ of $N$ is homotopy equivalent to $S^n$ or conn
Externí odkaz:
http://arxiv.org/abs/2105.07306
Autor:
Liokumovich, Yevgeny, Maximo, Davi
We construct singular foliations of compact three-manifolds $(M^3,h)$ with scalar curvature $R_h\geq \Lambda_0>0$ by surfaces of controlled area, diameter and genus. This extends Urysohn and waist inequalities of Gromov-Lawson and Marques-Neves.
Externí odkaz:
http://arxiv.org/abs/2012.12478
Publikováno v:
Ars Inveniendi Analytica (2022), Paper No. 2, 27 pp
We show that for a generic $8$-dimensional Riemannian manifold with positive Ricci curvature, there exists a smooth minimal hypersurface. Without the curvature condition, we show that for a dense set of 8-dimensional Riemannian metrics there exists a
Externí odkaz:
http://arxiv.org/abs/2007.11560
Publikováno v:
Vestnik RUDN. International Relations, Vol 23, Iss 2, Pp 322-338 (2023)
The study focuses on the perception of the Russian military presence in Africa. The 1990s and early 2000s saw a long break in Russian-African relations, linked to Russia’s priority of establishing a dialogue with Western countries. Largely as a res
Externí odkaz:
https://doaj.org/article/413926c6dc6a44aa84a79a6cf45b3aa2
