相关论文: Estimates of the Carath\'eodory metric on the symm…

We study the rigidity of maps between bounded symmetric domains that preserve the Carath\'eodory/Kobayashi distance. We show that such maps are only possible when the rank of the co-domain is at least as great as that of the domain. When…

This article considers isometries of the Kobayashi and Carath\'{e}od-ory metrics on domains in $ \mathbf{C}^n $ and the extent to which they behave like holomorphic mappings. First we prove a metric version of Poincar\'{e}'s theorem about…

We study the Carath\'{e}odory and Kobayashi metrics by way of the method of dual extremal problems in functional analysis. Particularly incisive results are obtained for convex domains.

We present an equality between the Bergman metric and Carath\'{e}odry metric.

We present the Carath\'eodory-Reiffen metric and the inner Carath\'eodory distance on generalized parabolas. It turns out that on such parabolas the Carath\'eodory distance is not inner.

We describe all proper holomorphic mappings of the symmetrized polydisc and study its geometric properties. We also apply the obtained results to the study of the spectral unit ball in $\MM_n(\CC^n)$.

It was recently shown that the Carath\'eodory and Teichm\"uller metrics on the Teichm\"uller space of a closed surface do not coincide. On the other hand, Kra earlier showed that the metrics coincide when restricted to a Teichm\"uller disk…

We show that on a certain class of bounded, complete Reinhardt domains in $\mathbb{C}^n$ that enjoy a lot of symmetries, the Carath\'eodory pseudo-distance and the geodesic distance of the complete K\"ahler-Einstein metric with Ricci…

In this paper, we estimate the boundary behavior of the Sibony metric near a pseudoconcave boundary point. We show that the metric blows up at a different rate than the Kobayashi metric.

Caratheodory's and Kobayashi's metrics on Teichmueller spaces of dimension two or more are never equal in the direction of any tangent vector defined by a separating cylindrical differential

We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance.

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…

Using the Maskit coordinates for Teichmuller space, we prove the existence of new families of one dimensional subspaces on which the Caratheodory and Kobayashi metrics agree.

Studying the behavior of real and complex geodesics we provide sharp estimates for the Kobayashi distance, the Lempert function, and the Carath\'eodory distance on $\mathcal{C}^{2,\alpha}$-smooth strongly pseudoconvex domains. Similar…

Bounded symmetric domains carry several natural invariant metrics, for example the Carath\'eodory, Kobayashi or the Bergman metric. We define another natural metric, from generalized Hilbert metric defined in [FGW20], by considering the…

This paper investigates problems in the characterization of the proximity of digital discs. Based on the $\mathcal{L}_1$-metric structure for the 2D digital plane and using a Jaccard-like metric, we determine numerical characters for…

We characterize all algebraic subsets of the tridisk that are Caratheodory sets, that is the intrinsic Caratheodory metric on the set equals the Caratheodory metric for the tridisk. We show that such sets are either retracts, or are…

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the…

The Caratheodory and Kobayashi metrics have proved to be important tools in the function theory of several complex variables. But they are less familiar in the context of one complex variable. Our purpose here is to gather in one place the…

It is a classical fact, that given an arbitrary n-dimensional convex body, there exists an appropriate sequence of Minkowski symmetrizations (or Steiner symmetrizations), that converges in Hausdorff metric to a Euclidean ball. Here we…