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ON THE INJECTIVITY RADIUS GROWTH OF COMPLETE NONCOMPACT RIEMANNNIAN MANIFOLDS
INJECTIVITY RADIUS GROWTH COMPLETE NONCOMPACT RIEMANNNIAN MANIFOLDS
2018/4/19
In this paper we introduce a global geometric invariant (M) related to injectivityradius to complete non-compact Riemannian manifolds and prove: If (Mn) > 1,then Mn is isometric to Rn when Ricci curva...
Radius of Close-to-convexity of Harmonic Functions
Coefficient inequality partial sums radius of univalence analytic univalent convex and starlike harmonic functions
2011/8/24
Abstract: Let ${\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\bar{g}$ in the unit disk ${\mathbb D}$, and let $K=H+\bar{G}$ denote the harmonic Koebe function...
Maximum spectral radius of graphs with given connectivity and minimum degree
connectivity spectral radius Combinatorics
2011/9/21
Abstract: Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most $k$, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order $n$ with $\kappa(G) \...
Random Walk on a Co-Compact Fuchsian Group: Behavior of the Green's Function at the Spectral Radius
hyperbolic group surface group randomwalk Green’s function Gromov boundary Martin boundary Ruelle operator theorem
2011/9/22
Abstract: It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also show...
Continuity of the cone spectral radius
Cone spectral radius, continuity, cone spectrum, nonlinear cone maps,fixed point index
2011/9/19
Abstract: This paper concerns the question whether the cone spectral radius of a continuous compact order-preserving homogenous map on a closed cone in Banach space depends continuously on the map. Us...
C*-algebras with the weak expectation property and a multivariable analogue of Ando's theorem on the numerical radius
C*-algebras the weak expectation property Ando's theorem the numerical radius
2011/8/23
Abstract: A classic theorem of T. Ando characterises operators that have numerical radius at most one as operators that admit a certain positive 2x2 operator matrix completion. In this paper we consid...
A Gel'fand-type spectral radius formula and stability of linear constrained switching systems
Joint/generalized spectral radius Gel’fand-type spectral-radius formula linear switched system asymptotic stability
2011/8/22
Abstract: Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix mu...
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
Laplacian matrix Laplacian spectral radius girth unicyclic graph
2011/1/18
In this paper we consider the following problem: Over the class of all simple con-nected unicyclic graphs on n vertices with girth g (n, g being fixed), which graph minimizes the Laplacian spectral ra...
Hypersurfaces with small extrinsic radius or large $\lambda_1$ in Euclidean spaces
Mean curvature Reilly inequality Laplacian Spectrum pinching results
2010/12/3
We prove that hypersurfaces of Rn+1 which are almost extremal for the
Reilly inequality on 1 and have Lp-bounded mean curvature (p > n) are Hausdorff close to a sphere, have almost constant mean cur...
On the numerical radius of operators in Lebesgue spaces
the numerical radius Lebesgue spaces
2010/11/24
We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|...
On the injectivity radius and tangent cones at infinity of gradient Ricci solitons
injectivity radius tangent cones infinity of gradient Ricci solitons
2011/1/18
A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at in nity of certain gradient Ricci sol...
Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates
Two-dimensional Larmor Radius approximation canonical gyrokinetic coordinates
2010/11/9
In this paper, we present some new results about the approximation of the Vlasov-Poisson system with a strong external magnetic field by the 2D finite Larmor radius model. The proofs within the prese...
Connectivity and Minimal Distance Spectral Radius of Graphs
Connectivity Spectral Radius of Graphs
2010/11/15
In this paper, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with $k$ cut vertices (respectively, $k$ cu...
Rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of vertices is connected by at least one path in which no two e...
The covering radius problem for sets of perfect matchings
Perfect matchings Lovasz local lemma
2010/11/30
Consider the family of all perfect matchings of the complete graph K2n with 2n vertices.Given any collection M of perfect matchings of size s, there exists a maximum number f(n; x) such that if s f(...