Related papers: Combinatorial rigidity of multicritical maps
We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained…
We develop a new approach to the study of the multipoint loci of holomorphic maps between complex manifolds. We relate the $k$-fold locus to the curvilinear component of the Hilbert scheme of $k$ points on the source space of the map, and…
In this note we present a short alternative proof of an estimate obtained by A.B.-Mantel, C.B. Muratov and T.M. Simon in [3] regarding the rigidity of degree {$\pm 1$} conformal maps of $\mathbb{S}^2$, i.e. its M\"obius transformations.
In the late 1980's Sullivan initiated a programme to prove quasisymmetric rigidity in one-dimensional dynamics: interval or circle maps that are topologically conjugate are quasisymmetrically conjugate (provided some obvious necessary…
Let M be a closed embedded minimal hypersurface in a Euclidean sphere of dimension n+1, we prove that it is strongly rigid. As applications we confirm the conjecture proposed by Choi and Schoen in [3] and the Chern conjecture for n less…
When the number of non-triangular faces adjacent to a vertex $v$ is less than or equal to three, the vertex $v$ will be called (\emph{combinatorially}) \emph{rigid}. We study the number of rigid vertices and suggest a conjecture on a…
We introduce a family of spaces called critical varieties. Each critical variety is a subset of one of the positroid varieties in the Grassmannian. The combinatorics of positroid varieties is captured by the dimer model on a planar…
We prove that two topologically conjugate bi-critical circle maps whose signatures are the same, and whose renormalizations converge together exponentially fast in the $C^2$-topology, are $C^1$ conjugate.
We introduce the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K. This natural problem applies to…
For a simplicial complex K on m vertices and simplicial complexes K1,...,Km a composed simplicial complex K(K1,...,Km) is introduced. This construction generalizes an iterated simplicial wedge construction studied by A. Bahri, M. Bendersky,…
In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic…
In this paper, the structure of the critical group of the graph $K_m\times C_n$ is determined, where $m, n\ge 3$.
In this paper, we introduce cosine Thurston maps. In particular, we construct postsingularly finite topological cosine maps and focus on such maps with strictly preperiodic critical points. We use the techniques of Hubbard, Schleicher, and…
A new elementary proof for a theorem of D. Burns and S. Krantz on the rigidity of the analytic self maps of the unit disc was recently discovered by L. Baracco, D. Zaitsev, and G. Zampieri. We use their argument to generalize Burns-Krantz…
An example of potential density of rational points on the second punctual Hilbert scheme of certain K3 surfaces is treated in detail. This is an amplification of some remarks made by O'Grady and Oguiso.
We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…
The notion of admissible pairs of rational homogeneous spaces of Picard number one and their rigidity in terms of the geometric substructures was formulated by Mok and Zhang. The rigidity is known for subdiagram type. While when the…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We provide the explicit combinatorial structure of the Kirillov-Reshetikhin crystals B^{r,s} of type D_n(1), B_n(1), and A_{2n-1}(2). This is achieved by constructing the crystal analogue sigma of the automorphism of the D_n(1) (resp.…
In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the…