Related papers: Graded Bridgeman dilogarithm identities on hyperbo…
We show that the number of simple closed geodesics of length bounded by L on a hyperbolic surface of genus g with c cusps and b boundary components grows roughly like L^{6g+2b+2c-6}. This has been conjectured for some time.
We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/<q>, where q is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
The goal of this work is to give new quantitative results about the distribution of semi-arithmetic hyperbolic surfaces in the moduli space of closed hyperbolic surfaces. We show that two coverings of genus $g$ of a fixed arithmetic surface…
We describe an algorithm for computing certain characteristic numbers of surface scrolls using degenerations. As a corollary we obtain a method for computing the corresponding Gromov-Witten invariants of Grassmannians.
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a…
In contrast to elliptic surfaces, the Fourier restriction problem for hypersurfaces of non-vanishing Gaussian curvature which admit principal curvatures of opposite signs is still hardly understood. In fact, even for 2-surfaces, the only…
We discuss questions of isospectrality for hyperbolic orbisurfaces, examining the relationship between the geometry of an orbisurface and its Laplace spectrum. We show that certain hyperbolic orbisurfaces cannot be isospectral, where the…
A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…
We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann loss', a new…
We exhibit the analogy between prime geodesics on hyperbolic Riemann surfaces and ordinary primes. We present new asymptotic counting results concerning pairs of prime geodesics whose homology difference is fixed.
We construct two classes of singular Kobayashi hyperbolic surfaces in $P^3$. The first consists of generic projections of the cartesian square $V = C \times C$ of a generic genus $g \ge 2$ curve $C$ smoothly embedded in $P^5$. These…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.
We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer…
In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods…
By building on former results and the cusp expansion algorithm, we construct strict transfer operator approaches for geometrically finite developable hyperbolic orbisurfaces of infinite area without cusps. Together with the cusp expansion…
In this article, we derive off-diagonal estimates of the Bergman kernel associated to tensor- products of the cotangent line bundle defined over a hyperbolic Riemann surface of finite volume.
We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact…
We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.