相关论文: An application of metric cotype to quasisymmetric …

In this paper, we study existence of isometric embedding of $S_q^m$ into $S_p^n,$ where $1\leq p\neq q\leq \infty$ and $n\geq m\geq 2.$ We show that for all $n\geq m\geq 2$ if there exists a linear isometry from $S_q^m$ into $S_p^n$, where…

We introduce the notion of cotype of a metric space, and prove that for Banach spaces it coincides with the classical notion of Rademacher cotype. This yields a concrete version of Ribe's theorem, settling a long standing open problem in…

We prove that an injection from the integer set into the real line admits a quasiconformal extension to the complex plane if and only if it is quasisymmetric.

We prove that a quotient of subspace of $C_p\oplus_pR_p$ ($1\le p<2$) embeds completely isomorphically into a noncommutative $L_p$-space, where $C_p$ and $R_p$ are respectively the $p$-column and $p$-row Hilbertian operator spaces. We also…

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

We give a sufficient condition for a projective metric on a subset of a Euclidean space to admit a bi-Lipschitz embedding into Euclidean space of the same dimension.

Given any $1 < q \le 2$, we use new free probability techniques to construct a completely isomorphic embedding of $\ell_q$ (equipped with its natural operator space structure) into the predual of a sufficiently large QWEP von Neumann…

We classify the Q-polynomial association schemes with $m_{1} = 4$ which are partially metric with respect to the nearest neighbourhood relation. An association scheme is partially metric with respect to a relation $R_1$ if the scheme graph…

We construct quasi-solvable quantum mechanical matrix models by employing two different methods, the one is universal enveloping algebra of Lie superalgebra and the other is N-fold supersymmetry. For the former we examine the q(2) and…

This is a short survey of Riemannian geometric applications of Lp-cohomology of thick spaces, p not equal to 2.

We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semisimple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a…

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. Assuming certain conditions on the fundamental group $\pi_1(M)$ we construct quasi-isometric embeddings of either free Abelian or…

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…

For every $p\in (0,\infty)$ we associate to every metric space $(X,d_X)$ a numerical invariant $\mathfrak{X}_p(X)\in [0,\infty]$ such that if $\mathfrak{X}_p(X)<\infty$ and a metric space $(Y,d_Y)$ admits a bi-Lipschitz embedding into $X$…

We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…

Let 1 \le p < q \le 2 and let M be any von Neumann algebra. We use recent techniques from free harmonic analysis to construct a completely isomorphic embedding of Lq(M) (equipped with its natural operator space structure) into Lp(A) for…

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…

We consider quasi-perfect codes in $\mathbb{Z}^n$ over the $\ell_p$ metric, $2 \leq p < \infty$. Through a computational approach, we determine all radii for which there are linear quasi-perfect codes for $p = 2$ and $n = 2, 3$. Moreover,…

In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-$k$-curved metrics}. Quasi-$k$-curved metrics generalize the metrics of space forms. We construct explicit…

We study the conformal metrics on $\R^{2m}$ with constant Q-curvature $Q$ having finite volume, particularly in the case $Q\leq 0$. We show that when $Q<0$ such metrics exist in $\R^{2m}$ if and only if $m>1$. Moreover we study their…