We show that the fundamental group of a ribbon disc complement in the four ball associated with certain prime dense and alternating surface arc projections are CAT(0) and δ-hyperbolic. Using this we produce an infinite class of free-by-cyclic CAT(0), δ-hyperbolic multi ribbon disc groups. AMS Subject classification: 57M05, 57M50, 20F65, 20F67.

Surface plasmon polaritons usually exist on a few suitable plasmonic materials; however, nanostructured plasmonic metamaterials allow a much broader range of optical properties to be designed. Here, bottom-up and top-down nanostructuring are combined, creating hyperbolic metamaterial-based photonic crystals termed hyperbolic polaritonic crystals, allowing free-space access to the high spatial f...

We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution result was first obtained in the early 1980s by Dani and Smillie [DS84] and later reappeared as an illustrative special case [Rat92] of Ratner’s work [Rat91-Rat94] on the equidistribution of unipot...

This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinh t, cosh t, tk−3, tk−4, . . . , t,1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of cur...

We consider dissipative Dyakonov plasmon-polaritons as surface waves propagating along the plane boundary of a hyperbolic metamaterial with an arbitrary orientation crystallographic axis. Conditions for existence fast, slow, gliding flowing, forward and backward are found. A waveguide in form asymmetric layer is also considered. An expression density electromagnetic energy such given.