No abstract uploaded!

We give a detailed proof of Siu’s theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in $\mathbb{C}^{n}, n \geq3$ , is not subelliptic.

No abstract uploaded!

Traditional point cloud registration methods require large overlap between scans, which imposes strict constraints on data acquisition. To facilitate registration, users have to carefully position scanners to ensure sufficient overlap. In this work, we propose to use high-level structural information (i.e., plane/line features and their inter-relationship) for registration, which is capable of registering point clouds with small overlap, allowing more freedom in data acquisition. We design a novel plane/linebased descriptor dedicated to establishing structure level correspondences between point clouds. Based on this descriptor, we propose a simple but effective registration algorithm. We also provide a dataset of real-world scenes containing a larger number of scans with a wide range of overlap. Experiments and comparisons with state-of-the-art methods on various datasets reveal that our method is superior to existing techniques. Though the proposed algorithm outperforms state-of-the-art methods on the most challenging dataset, the point cloud registration problem is still far from being solved, leaving significant room for improvement and future work.

There are two important statements regarding the Trautman-Bondi mass at null infinity: one is the positivity, and the other is the Bondi mass loss formula, which are both global in nature. The positivity of the quasi-local mass can potentially lead to a local description at null infinity. This is confirmed for the Vaidya spacetime in this note. We study the Wang-Yau quasi-local mass on surfaces of fixed size at the null infinity of the Vaidya spacetime. The optimal embedding equation is solved explicitly and the quasi-local mass is evaluated in terms of the mass aspect function of the Vaidya spacetime.