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HARNACK INEQUALITY AND HYPERBOLICITY FOR SUBELLIPTIC p-LAPLACIANS WITH APPLICATIONS TO PICARD TYPE THEOREMS
HARNACK INEQUALITY HYPERBOLICITY
2015/8/26
Let M be a complete non-compact Riemannian manifold. For p ∈ (1,+∞),
let Δp be the p-Laplace operator on M. One says that M is p-hyperbolic
if there exists a Green function for Δp (see [Ho1,2]); oth...
High Order Moment Closure with Global Hyperbolicity of Vlasov-Maxwell Equations
Moment closure Vlasov-Maxwell equation Boltzmann equation Ex-tended magnetohydrodynamics
2014/9/26
In this paper, we derive the extended magnetohydrodynamic models based on the
moment closure of the Vlasov-Maxwell equation. We adopt the Grad type moment
expansion which was firstly proposed in [12...
On Hyperbolicity of 13-Moment System
Hyperbolicity of 13-Moment System hyperbolicity region
2014/9/26
We point out that the thermodynamic equilibrium is not an interior point of the
hyperbolicity region of Grad’s 13-moment system. With a compact expansion of the
phase density, which is compacter tha...
Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
hyperbolic polynomials hyperbolicity cones spectrahedral cones elementary symmetric polynomials spanning trees matrix-tree theorem
2012/4/16
We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix--tree theore...
Non-Uniform hyperbolicity for infinite dimensional cocycles
Random operators dominated splitting multiplicative ergodic theorem Lyapunov exponents
2011/9/14
Abstract: Let H be an infinite dimensional separable Hilbert space, X a compact Hausdorff space and f : X \rightarrow X a homeomorphism which preserves a Borel ergodic measure which is positive on non...
Hyperbolicity of the complex of free factors
Hyperbolicity of the complex free factors Group Theory
2011/9/13
Abstract: We prove that the complex of free factors of a free group of finite rank is hyperbolic.
Characterization of hyperbolicity and generalized shadowing lemma
Hyperbolicity Lyapunov exponents shadowing Anosov maps
2011/9/13
Abstract: J. Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle o...
A survey on hyperbolicity of projective hypersurfaces
hyperbolicity of projective hypersurfaces Algebraic Geometry Complex Variables
2011/8/26
Abstract: These are lecture notes of a course held at IMPA, Rio de Janiero, in september 2010: the purpose was to present recent results on Kobayashi hyperbolicity in complex geometry. Our ultimate go...
Hyperbolicity and identification of Berge knots of types VII and VIII
doubly primitive knot Alexander polynomial Reidemeister torsion
2011/8/23
Abstract: T. Saito and M. Teragaito asked in their paper whether Berge knots of type VII, which can be situated on the fiber surface of the lefthand trefoil, are hyperbolic, and showed that some infin...
Hyperbolicity of the invariant sets for the real polynomial maps
Cantor set Complex dynamic Hyperbolic Logistic map Polynomial map
2011/2/25
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
2010/11/22
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...
Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps
Regular hyperbolicity dominant energy condition Lagrangian theory
2010/11/19
The goal of the present paper is three-fold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories. Second is to provide fu...
The topology of balls and Gromov hyperbolicity of Riemann surfaces
Topology of balls uniformly separated sets Riemann surfaces Gromov hyperbolicity
2010/12/9
For each k > 0 we find an explicit function fk such that the topology of S inside the ball
BS(p, r) is ‘bounded’ by fk(r) for every complete Riemannian surface (compact or noncompact) S with K W...
A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle
geometric criterion non-uniform hyperbolicity Kontsevich--Zorich cocycle
2010/12/10
We prove a geometric criterion on a SL(2,R)-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the ...
Lack of Spectral Gap and Hyperbolicity in Asymptotic Erdös-Renyi Random Graphs
Spectral Gap Hyperbolicity Asymptotic Erdö s-Renyi Random Graphs
2010/12/14
In this work, we prove the absence of a spectral gap for the normalized Laplacian of the Erdos-Renyi random graph G(n; p) when p = d n for d > 1 as n ! 1. We also prove that for any positive the Er...