Related papers: The minimum volume of subspace trades
Let $T\subset \R^{m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partial T$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed intial point $A\in X$, a…
We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stability thresholds for valuations, and then showing that a…
An undirected biclique $K_{a,b}$ is a graph with vertices partitioned into two sets: a set $A$ containing $a$ vertices and a set $B$ containing $b$ vertices such that every vertex in set $A$ is connected to every vertex in set $B$, and such…
We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.
We prove that a minimal disc in a CAT(0) space is a local embedding away from a finite set of "branch points". On the way we establish several basic properties of minimal surfaces: monotonicity of area densities, density bounds, limit…
A $t$-$(n,k,\lambda)$ design over $\F_q$ is a collection of $k$-dimensional subspaces of $\F_q^n$, called blocks, such that each $t$-dimensional subspace of $\F_q^n$ is contained in exactly $\lambda$ blocks. Such $t$-designs over $\F_q$ are…
In this paper, we prove that for any closed 4-dimensional Riemannian manifold $M$ with trivial first homology group, if the Ricci curvature $|Ric|\leq3$, the diameter $diam(M)\leq D$ and the volume $vol(M)>v>0$, then the area of a smallest…
A subset of a metric space is a k-distance set if there are exactly k non-zero distances occuring between points. We conjecture that a k-distance set in a d-dimensional Banach space (or Minkowski space), contains at most (k+1)^d points,…
We study the topology and dynamics of subshifts and tiling spaces associated to non-primitive substitutions in one dimension. We identify a property of a substitution, which we call tameness, in the presence of which most of the possible…
This paper is devoted to construct a minimal toric embedded resolution of a rational singularity via jet schemes. The minimality is reached by extending the concept of the profile of a simplicial cone given in 6.
We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle…
Upper and lower bounds are derived for the quantity in the title, which is tabulated for modest values of $n$ and $k.$ An application to graphs with many cycles is given.
A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial…
A Banach space with a Schauder basis is said to be $\alpha$-minimal for some countable ordinal $\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\alpha$. We prove a dichotomy that…
In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. $(X,T)$ and the t.d.s. $(K(X),T_K)$ induced on the hyperspace $K(X)$ of all compact subsets of $X$, and provide some characterizations.…
Let K be a field of characteristic different from 2 and let V be a vector space of dimension n over K. Let M be a non-zero subspace of symmetric bilinear forms defined on V x V and let r=rank(M) denote the set of different positive integers…
The super Virasoro minimal string is defined by coupling spacelike and timelike super Liouville theories on the worldsheet. There are four different theories 0A$^\pm$ and 0B$^\pm$ depending on discrete choices on the worldsheet. We show…
We show that the combinatorial types of the links of the vertices in the edgewise triangulation $T_{k,q}$ of a $(k-1)$-simplex are encoded by the partitions of $k$. Each of these complexes is isomorphic to a subcomplex of the barycentric…
We show that the minimal volume of surfaces of log general type, with non-empty non-klt locus on the ample model, is $\frac{1}{825}$. Furthermore, the ample model $V$ achieving the minimal volume is determined uniquely up to isomorphism.…
It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…