A quantitative finite-dimensional krivine theoremSpringer Science and Business Media LLC - Tập 50 - Trang 1-12 - 1985
D. Amir, V. D. Milman
Measure concentration arguments are applied to get a power-type estimate for the
dimension of almostl p subspaces of isomorphs ofl p n and for the length of
almost-symmetric sequences under a nonlinear-type condition.
Compounds of asymmetric convex bodiesSpringer Science and Business Media LLC - Tập 19 - Trang 349-358 - 1974
R. J. Cook
Mahler obtained inequalities relating an0-symmetric convex body with its
compounds. These results are extended to asymmetric convex bodies.
Residual properties of free groups, IIISpringer Science and Business Media LLC - Tập 77 - Trang 65-81 - 1992
T. S. Weigel
In this paper we want to prove the following theorem: Letx be an infinite set of
non-abelian finite simple groups. Then the free groupF 2 on 2 generators is
residuallyx. This answers a question first posed by W. Magnus and later by A.
Lubotzky [9], Yu. Gorchakov and V. Levchuk [4].
Knot exteriors with all possible meridional essential surfacesSpringer Science and Business Media LLC - Tập 225 - Trang 909-924 - 2018
João M. Nogueira
We show the existence of infinitely many knots where each exterior contains
meridional essential surfaces of independently unbounded genus and number of
boundary components. In particular, we construct examples of knot exteriors each
of which has all possible compact orientable surfaces embedded as meridional
essential surfaces. From these results, we also prove the existence of a
hyperbolic knot ... hiện toàn bộ
Equilateral triangles in subsets of ℝd of large Hausdorff dimensionSpringer Science and Business Media LLC - Tập 231 - Trang 123-137 - 2019
Alex Iosevich, Bochen Liu
We prove that subsets of ℝd, d ≥ 4 of large enough Hausdorff dimensions contain
vertices of an equilateral triangle. It is known that additional hypotheses are
needed to assure the existence of equilateral triangles in two dimensions (see
[3]). We show that no extra conditions are needed in dimensions four and higher.
The three dimensional case remains open. Some interesting parallels exist
betwee... hiện toàn bộ