Sentence examples for on a hyperbolic surface from inspiring English sources

Mirzakhani's early work concerns closed geodesics on a hyperbolic surface.

A circle on a hyperbolic surface has an exponentially increasing circumference, as opposed to the familiar Euclidean situation where circle circumference grows quadratically with respect to its radius.

However, in 1955 the Dutch mathematician Nicolaas Kuiper proved the existence of a complete hyperbolic surface, and in the 1970s the American mathematician William Thurston described the construction of a hyperbolic surface.

In this paper, we introduce the norm squares Bp for Qp spaces on a hyperbolic Riemann surface R so that Bp(f)="1 for 0⩽p⩽∞ if R is the unit disk and f is the identity function, and prove the sharp inequality Bp(f)⩽Bq(f) for 0⩽q<p⩽∞.

We have shown how, for example, the model produces pentagonal grids on a spherical surface and heptagonal ones on a hyperbolic one (Urdapilleta et al., 2015).

Sometimes properties of a fixed hyperbolic surface can be better understood by studying the moduli space that parameterises all hyperbolic structures on a given topological surface.

These are geometric objects whose points each represent a different hyperbolic surface.

The question of location and distribution of the zeros of the Selberg Zeta function associated to a noncompact hyperbolic surface attracted attention of the mathematical community in 2014 when numerical experiments by D. Borthwick showed that for certain surfaces zeros seem to lie on smooth curves.

Obviously, a value has a significant influence on the shape of the hyperbolic surface.

Suita's conjecture can be stated as follows: [50] Let (X) be a hyperbolic Riemann surface.

In the Klein-Beltrami model (shown in the figure, top left), the hyperbolic surface is mapped to the interior of a circle, with geodesics in the hyperbolic surface corresponding to chords in the circle.