17 citations · 55 across the 12 of their papers we have counts for
12 papers
Boundary metric of Epstein-Penner convex hull and discrete conformality
Xin Nie
The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a polyhedral convex body in the Minkowski space. It works in the de Sitter an…
On circle patterns and spherical conical metrics
Xin Nie
The Koebe-Andreev-Thurston circle packing theorem, as well as its generalization to circle patterns due to Bobenko and Springborn, holds for Euclidean and hyperbolic metrics possib…
Cyclic Higgs bundles and minimal surfaces in pseudo-hyperbolic spaces
Xin Nie
We introduce a type of minimal surface in the pseudo-hyperbolic space (with even) or (with odd) associated to cyclic $\mathrm{SO}_…
Hypersurfaces of constant Gauss-Kronecker curvature with Li-normalization in affine space
Xin Nie, Andrea Seppi
For convex hypersurfaces in the affine space (), A.-M.\ Li introduced the notion of -normal field as a generalization of the affine normal field. By s…
Affine deformations of quasi-divisible convex cones
Xin Nie, Andrea Seppi
For any subgroup of obtained by adding a translation part to a subgroup of which is the fundamental group…
Large genus asymptotics for lengths of separating closed geodesics on random surfaces
Xin Nie, Yunhui Wu, Yuhao Xue
In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus with respect to the Weil-Petersson measure on the moduli space .…
Limit polygons of convex domains in the projective plane
Xin Nie
For any sequence of properly convex domains in the real projective plane such that the zeros of Pick differentials have bounded multiplicity and get further and further apart, we d…
Regular domains and surfaces of constant Gaussian curvature in three-dimensional affine space
Xin Nie, Andrea Seppi
Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In dimension…
Poles of cubic differentials and ends of convex -surfaces
Xin Nie
The affine sphere construction gives, on any oriented surface, a one-to-one correspondence between convex -structures and holomorphic cubic differentials. Generalizi…
Meromorphic cubic differentials and convex projective structures
Xin Nie
Extending the Labourie-Loftin correspondence, we establish, on any punctured oriented surface of finite type, a one-to-one correspondence between convex projective structures with…
The quasi-Poisson Goldman formula
Xin Nie
We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formul…
On the Hilbert geometry of simplicial Tits sets
Xin Nie
The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that i…