相关论文: Uniform Perfectness, Geodesic Richness, and Rigidi…

Let $ T:[0,1]\to[0,1] $ be an expanding Markov map with a finite partition. Let $ \mu_\phi $ be the invariant Gibbs measure associated with a H\"older continuous potential $ \phi $. In this paper, we investigate the size of the uniform…

We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…

Tight geodesics were introduced by Masur-Minsky in [17]. They and their hierarchies have been a powerful tool in the study of the curve complex, mapping class groups, Teichm\"uller spaces, and hyperbolic 3-manifolds. In the same paper, they…

Let $\Omega\subset\mathbb{R}^{n+1}$, $n\geq2$, be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ in divergence form associated with a matrix $A$ with…

Let $L:[0,1]\setminus\{d\}\rightarrow [0,1]$ be a one-dimensional Lorenz like expanding map ($d$ is the point of discontinuity), $\mathcal{P}=\{ (0,d),(d,1) \}$ be a partition of $[0,1]$ and $C^{\alpha}([0,1],\mathcal{P})$ the set of…

From the work of Phong and Sturm in 2007, for a polarised projective manifold and an ample test configuration, one can associate the geodesic ray of plurisubharmonic metrics on the polarising line bundle using the solution of the…

Motivated by a recent work of X. Chen and M. Zhu (Commun. Math. Stat., 1 (2013) 369-385), we establish a Trudinger-Moser inequality on compact Riemannian surface without boundary. The proof is based on blow-up analysis together with…

For every algebraic number $\kappa$ on the unit circle which is not a root of unity we prove the existence of a strict sequence of algebraic numbers whose height tends to zero, such that the averages of the evaluation of $f_\kappa(z)=\log|z…

We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of finite area. These sharp curvature-free upper bounds are…

We consider a group G of isometries acting on a (not necessarily geodesic) delta-hyperbolic space X and possessing a radial limit set of full measure within its limit set. For any continuous quasiconformal measure w supported on the limit…

We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

We introduce a flexible, categorical framework for large-scale geometry that clarifies basic behaviour of the metric Rips filtration and streamlines some constructions in geometric group theory. The paper has two main parts. First, we…

We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building…

In this paper, first of all, according to Lu's and Zhang's works about the curvature of the Bergman metric on a bounded domain and the properties of the squeezing functions, we obtain that Bergman curvature of the Bergman metric on a…

In this article, we prove that there exists a unique perimeter minimizer among all piecewise smooth simple closed curves in $M_{\kappa}^2$ enclosing area $A > 0$ $(A \leq 2{\pi}$ if ${\kappa} = 1)$, and it is a circle in $M_{\kappa}^2$ of…

We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One is that they are sublinearly contracting; the other is that…

We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi-geodesic rays and the space is equipped with a topology that is naturally invariant…

The Gardiner-Masur compactification of Teichm\"uller space is homeomorphic to the horofunction compactification of the Teichm\"uller metric. Let $\xi$ and $\eta$ be a pair of boundary points in the Gardiner-Masur compactification that fill…

The $\kappa$-topologies on the spaces $\mathscr{D}_{L^p}$, $L^p$ and $\mathscr{M}^1$ are defined by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre-)dual spaces. In many cases it is more…