Characterizations of John spaces

The main purpose of this paper is to study the characterizations of John spaces. We obtain five equivalence characteristics for length John spaces. As an application, we establish a dimension-free quasisymmetric invariance of length John spaces.This result is new also in the case of the Euclidean space.Comment: Monatshefte fur Mathematik;201

Uniformizing Gromov hyperbolic spaces and Busemann functions

By introducing a new metric density via Busemann function, we establish an unbounded uniformizing Gromov hyperbolic spaces procedure which is an analogue of a recent work of Bonk, Heinonen and Koskela in \cite{BHK}. Then we show that there is a one-to-one correspondence between the quasi-isometry classes of proper geodesic Gromov hyperbolic spaces that are roughly starlike with respect to the points at the boundaries of infinity and the quasi-similarity classes of unbounded locally compact uniform spaces. As applications, we establish Teichm\"{u}ller's displacement theorem for roughly quasi-isometry in Gromov hyperbolic spaces, and explain the connections to the bilipschitz extensions of certain Gromov hyperbolic spaces. By using our uniformizing procedure, we also provide a new proof for V\"{a}is\"{a}l\"{a}-Heinonen-N\"{a}kki's Theorem in the setting of metric spaces. Moreover, we obtain the quasisymmetry from local to global on uniform metric spaces

Gromov hyperbolization of unbounded noncomplete spaces and Hamenst\"adt metric

In this note, we investigate the hyperbolizations of unbounded noncomplete metric spaces associated to three hyperbolic type metrics: hyperbolization metric $h$ introduced by Ibragimov, $\widetilde{j}$-metric and the quasihyperbolic metric $k$. We show that for such a space $(X,d)$, $\partial X\cup\{\infty\}$, $\partial_h X$, $\partial_{\widetilde{j}}X$ are mutually quasisymmetrically equivalent with respect to the metric $d$ and certain Hamenst\"adt metrics on the boundaries at infinity of these two hyperbolic spaces, respectively. Moreover, $\partial X\cup\{\infty\}$ is also quasisymmetrically equivalent to Gromov boundary $\partial_k X$ equipped with certain Hamenst\"adt metric whenever $X$ is uniform. As an application, we get a characterization of unbounded uniform domains in Banach spaces

Bidirectional-Convolutional LSTM Based Spectral-Spatial Feature Learning for Hyperspectral Image Classification

This paper proposes a novel deep learning framework named bidirectional-convolutional long short term memory (Bi-CLSTM) network to automatically learn the spectral-spatial feature from hyperspectral images (HSIs). In the network, the issue of spectral feature extraction is considered as a sequence learning problem, and a recurrent connection operator across the spectral domain is used to address it. Meanwhile, inspired from the widely used convolutional neural network (CNN), a convolution operator across the spatial domain is incorporated into the network to extract the spatial feature. Besides, to sufficiently capture the spectral information, a bidirectional recurrent connection is proposed. In the classification phase, the learned features are concatenated into a vector and fed to a softmax classifier via a fully-connected operator. To validate the effectiveness of the proposed Bi-CLSTM framework, we compare it with several state-of-the-art methods, including the CNN framework, on three widely used HSIs. The obtained results show that Bi-CLSTM can improve the classification performance as compared to other methods