Related papers: On the Isomorphic Embedding of Rectangular Grids i…

We consider spherical quadrangulations -- spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 -- in which all vertices have degree 3 or 4. Interpreting each degree 4 vertex as a…

This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…

We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…

This is a survey paper. We explain the known constructions for two geometrically different classes of examples of compact Riemannian 7-manifolds with holonomy G2. One method uses resolutions of singularities of appropriately chosen…

In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $L_1$. As a corollary, we obtain that all planar graphs which are 1-skeletons of planar non-positively…

Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem…

Let $G$ and $H$ be graphs, with $|V(H)|\geq |V(G)| $, and $f:V(G)\rightarrow V(H)$ a one to one map of their vertices. Let $dilation(f) = max\{ dist_{H}(f(x),f(y)): xy\in E(G) \}$, where $dist_{H}(v,w)$ is the distance between vertices $v$…

The classical Heawood inequality states that if the complete graph $K_n$ on $n$ vertices is embeddable in the sphere with $g$ handles, then $g \ge\dfrac{(n-3)(n-4)}{12}$. A higher-dimensional analogue of the Heawood inequality is the…

Let $i:X\hookrightarrow Y$ be a closed embedding of smooth algebraic varieties. Denote by $N$ the normal bundle of $X$ in $Y$. We describe the construction of two Lie-type structures on the shifted bundle $N[-1]$ which encode the…

A pseudocircle is a simple closed curve on some surface; an arrangement of pseudocircles is a collection of pseudocircles that pairwise intersect in exactly two points, at which they cross. Ortner proved that an arrangement of pseudocircles…

In this paper fundamental nonlinear geometries of Lebesgue sequence spaces are studied in their quantitative aspects. Applications of this work are a positive solution to the strong embeddability problem from $\ell_q$ into $\ell_p$…

We review the regular tilings of d-sphere, Euclidean d-space, hyperbolic d-space and Coxeter's regular hyperbolic honeycombs (with infinite or star-shaped cells or vertex figures) with respect of possible embedding, isometric up to a scale,…

We prove that if an RCD space has a regular isometric immersion in a Euclidean space, then the immersion is a locally bi-Lipschitz embedding map. This result leads us to prove that if a compact non-collapsed RCD space has an isometric…

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and…

We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to…

We study the problem of Embedding Wirelength of $n$-dimensional Hypercube $Q_n$ into Cylinder $C_{2^{n_1}}\times P_{2^{n_2}}$, where $n_1+ n_2=n$, called EWHC. We show that such wirelength corresponding to Gray code embedding is…

A stacking operation adds a $d$-simplex on top of a facet of a simplicial $d$-polytope while maintaining the convexity of the polytope. A stacked $d$-polytope is a polytope that is obtained from a $d$-simplex and a series of stacking…

Let G be a graph and let N_1, ..., N_k be k independent sets in G. The graph G is a k-probe cograph if G can be embedded into a cograph by adding edges between vertices that are contained in the same independent set. We show that there…

I construct "fake algebraic curves" in $Cp^2$. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces $F\subset Cp^2$ homeomorphic to a non-singular…

Li et al. in [Inf. Process. Lett. 77 (2001) 35--41] proposed the shuffle cube $SQ_{n}$ as an attractive interconnection network topology for massive parallel and distributed systems. By far, symmetric properties of the shuffle cube remains…