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The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the…
We apply the technique of parameter-splitting to existing cosmological data sets, to check for a generic failure of dark energy models. Given a dark energy parameter, such as the energy density Omega_Lambda or equation of state w, we split…
The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a…
We construct a minimal model within the general class of Pyramid Schemes, which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low…
The Circle Pattern Theorem characterizes the existence and rigidity of circle patterns with prescribed intersection angles on simplicial triangulations of closed surfaces. In this paper we extend the theorem to quasi-simplicial…
In this paper we find necessary and sufficient conditions for the weak convergence of c-free convolution of pairs of measures, where the measures are assumed to be infinitesimal and their support may be unbounded. These results are obtained…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
We give a sufficient condition on a sequence of uniformly bounded $\omega$-plurisubharmonic functions, $\omega$ being a Hermitian metric, for which the sequence of associated Monge-Amp\`ere measures converges weakly. This criterion can be…
We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove the results of Troyanov and Luo-Tian regarding existence and uniqueness of conformal spherical metrics on the Riemann sphere with prescribed cone angles in the…
Let $M$ be a complex manifold which admits an exhaustion by open subsets $M_j$ each of which is biholomorphic to a fixed domain $\Omega \subset \mathbb C^n$. The main question addressed here is to describe $M$ in terms of $\Omega$. Building…
In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum then the manifold is compact and its diameter is bounded in terms of the infimum. Subsequently the curvature hypothesis has been…
We propose two new proofs of the Pythagorean theorem via area rearrangement arguments starting from very simple geometric configurations. The constructions depend on an angular parameter, each choice of which yields a proof. For specific…
In response to the comment made by Dr. Shirakura {\it et al} (cond-mat/0011235), we explain that their scaling forms of the order parameter distribution are inadequate. We then present an appropriate scaling form of the order parameter…
While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case of unilateral rapidly decreasing functions. To address this…
The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field…
In [SWW], S. Seto, L. Wang and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter,…
We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a…
W. M. Hirsch formulated a beautiful conjecture on diameters of convex polyhedra.I suggest a new viewpoint with the deformation and moduli of polytopes.
A metric measure space is a metric space with a Borel measure. In Gromov's theory of metric measure spaces, there are important invariants called the partial diameter and the observable diameter. We obtain the result that the partial…
In this paper, we introduce the notions of proximally completeness, proximally closedness and proximally continuity and utilize the same to prove a result on existence and uniqueness of best proximity points in the setting of metric space…