We consider the question of which right-angled Artin groups contain closed hyperbolic surface subgroups. It is known that a right-angled Artin group A(K) has such a subgroup if its defining graph K contains an n-hole (i.e. an induced cycle of length n) with n ≥ 5. We construct another eight “forbidden” graphs and show that every graph K on ≤ 8 vertices either contains one of our examples, or co...

We study the radiative heat flux between two nanoparticles in close vicinity to natural hyperbolic material hBN with its optical axis oriented parallel interface. show that can be efficiently modulated when rotating due coupling highly directional surface modes hBN. Finally, we discuss thickness and distance dependence of this effect.

Elliptic and hyperbolic partial differential equation methods for generating both surface and volume structured grids have been implemented in the Gridgen software system. Their implementation provides the means by which very high quality quad and hex grids can be generated for computational fluid dynamics (CFD). The grids, in turn, provide the basis for highly accurate CFD simulations of visco...

This paper describes some properties of a certain fibered hyperbolic 3manifold which arises ”in nature”; that is, as the cover of a closed manifold constructed by other means. Among other things, the main theorem answers in the affirmative the question of whether it is possible for a fibered hyperbolic manifold to be a double across a connected surface. (We first heard this question from Alan R...

Let f : M → M be a C-diffeomorphism, r ≥ 1, defined on a closed manifold M . We prove that if M is a surface and K ⊂ M is a compact invariant set such that TKM = E ⊕ F is a dominated splitting then f/K is entropy expansive. Moreover C generically in any dimension, isolated homoclinic classes H(p), p hyperbolic, are entropy expansive. Conversely, if there exists a C neighborhood U of a surface d...

The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon’s Conjecture: A hyperbolic group G (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic ...

A hyperbolic curve is an algebraic curve obtained by removing r points from a smooth, proper curve of genus g, where g and r are nonnegative integers such that 2g−2+r > 0. If X is a hyperbolic curve over the field of complex numbers C, then X gives rise in a natural way to a Riemann surface X . As one knows from complex analysis, the most fundamental fact concerning such a Riemann surface (due ...

In addition to being packed with fundamental material important for every beginner in complex analysis, in expeditious and intuitive terms this little book transports the reader through a range of interesting topics in one-dimensional hyperbolic geometry, discrete subgroups, holomorphic dynamics and iterated function systems. In chapter after chapter, one quickly arrives at open problems and ar...