Related papers: Nonnegative Grassman Chambers are Balls

In this note, we provide a starlike and normal tiling in any separable Banach space. That means, there are positive constants r and R (not depending on the separable Banach space) such that every tile of this tiling is starlike, contains a…

We survey some properties of Gromov--Hausdorff--Prokhorov convergent sequences $(\mathsf{X}_n, d_{\mathsf{X}_n}, \nu_{\mathsf{X}_n})_{n \ge 1}$ of random compact metric spaces equipped with Borel probability measures. We formalize that if…

It is proven that the relativistic charged ball with its charge less than its mass (in natural units) cannot have a non-singular static configuration while its radius approaches its external horizon size. This conclusion does not depend on…

We produce a detailed map of the perturbed surface density of neutral hydrogen in the outer Milky Way disk demonstrating that the Galaxy is a non-axisymmetric multi-armed spiral. Spiral structure in the southern half of the Galaxy can be…

We have discovered a "little" gap in our proof of the sharp conjecture that in $\mathbb{R}^n$ with volume and perimeter densities $r^m$ and $r^k$, balls about the origin are uniquely isoperimetric if $0 < m \leq k - k/(n+k-1)$, that is, if…

We show that the totally nonnegative part of a partial flag variety (in the sense of Lusztig) is homeomorphic to a closed ball.

By dividing a sample of 48 long-duration gamma-ray bursts (GRBs) into four groups with redshift from low to high and fitting each group with the Amati relation log Eiso = a + b log Epeak, I find that parameters a and b vary with the mean…

We prove that the Teichm\"uller space of surfaces of genus $\mathbf{g}$ with $\mathbf{p}$ punctures contains balls which are not convex in the Teichm\"uller metric whenever $3\mathbf{g}-3+\mathbf{p} > 1$.

We show that the totally nonnegative part of a partial flag variety $G/P$ (in the sense of Lusztig) is a regular CW complex, confirming a conjecture of Williams. In particular, the closure of each positroid cell inside the totally…

We establish a general criterion for the existence of convex sets of fixed shape as, e.g., balls of a given radius, of maximal probability on Banach spaces. We also provide counterexamples showing that their existence my fail even in some…

Let G=SL(n,R) with n>5. We construct examples of lattices Gamma of G, subgroup A of the diagonal group and points x in G/Gamma such that the closure of the orbit Ax is not homogeneous but does not factors through the action of a…

Let $\pi$ be a finitely presented group. If h is a non trivial homology class in Hn($\pi$; Z), a theorem of Gromov (see [Gro83], 6) asserts the existence of regular geometric cycles which represent h, whose relative systolic volume is as…

We propose to use high-redshift long $\gamma$-ray bursts (GRBs) as cosmological tools to constrain the amount of primordial non-Gaussianity in the density field. By using numerical, N-body, hydrodynamic, chemistry simulations of different…

The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as positroids and plabic graphs. Remarkably, the same combinatorial…

A spectroscopically detected Lyman alpha emitting halo at redshift 3.216 in the GOODS-N field is found to reside at the convergence of several Lyman alpha filaments. HST images show that some of the filaments are inhabited by galaxies.…

We prove that three spaces of importance in topological combinatorics are homeomorphic to closed balls: the totally nonnegative Grassmannian, the compactification of the space of electrical networks, and the cyclically symmetric…

Most fully developed galaxies have a vivid spiral structure, but the formation and evolution of the spiral structure are still an enigma in astrophysics. In this paper, according to the standard Newtonian gravitational theory and some…

For any compact set $K \subseteq \mathbb{R}^3$ we define a number $r(K)$ that is either a nonnegative integer or $\infty$. Intuitively, $r(K)$ provides some information on how wildly $K$ sits in $\mathbb{R}^3$. We show that attractors for…

My conviction is explained that none of the daily gamma-ray bursts comes from cosmic distances. In particular, nearby reflection nebulae have been mistaken for host galaxies.

Deep HI observations of the outer parts of disc galaxies demonstrate the frequent presence of extended, well-developed spiral arms far beyond the optical radius. To understand the nature and the origin of such outer spiral structure, we…