Purpose Accurate segmentation of lung and infection in COVID‐19 computed tomography (CT) scans plays an important role in the quantitative management of patients. Most of the existing studies are based on large and private annotated datasets that are impractical to obtain from a single institution, especially when radiologists are busy fighting the coronavirus disease. Furthermore, it is hard to compare current COVID‐19 CT segmentation methods as they are developed on different datasets, trained in different settings, and evaluated with different metrics. Methods To promote the development of data‐efficient deep learning methods, in this paper, we built three benchmarks for lung and infection segmentation based on 70 annotated COVID‐19 cases, which contain current active research areas, for example, few‐shot learning, domain generalization, and knowledge transfer. For a fair comparison among different segmentation methods, we also provide standard training, validation and testing splits, evaluation metrics and, the corresponding code. Results Based on the state‐of‐the‐art network, we provide more than 40 pretrained baseline models, which not only serve as out‐of‐the‐box segmentation tools but also save computational time for researchers who are interested in COVID‐19 lung and infection segmentation. We achieve average dice similarity coefficient (DSC) scores of 97.3%, 97.7%, and 67.3% and average normalized surface dice (NSD) scores of 90.6%, 91.4%, and 70.0% for left lung, right lung, and infection, respectively. Conclusions To the best of our knowledge, this work presents the first data‐efficient learning benchmark for medical image segmentation, and the largest number of pretrained models up to now. All these resources are publicly available, and our work lays the foundation for promoting the development of deep learning methods for efficient COVID‐19 CT segmentation with limited data.

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Abstract. In this paper, we investigate the hyperbolic Gauss map of a complete CMC-1 surface in H 3 (−1), and prove that it cannot omit more than four points unless the surface is a horosphere. IntroductionIn minimal surface theory, the value distribution of the Gauss map has been studied for a long time. 3 . An interesting feature is that there exists a family of absolutely area-minimizing hypersurfaces in H n and only one of them is totally geodesic (see [7]). The question seems to be how to raise an adequate Bernstein problem in hyperbolic space. Professor Y. L. Xin pointed out to me that the striking work done by R. Bryant [1] supplies a framework to solve the Bernstein problem in hyperbolic space.In this paper, we shall be concerned with the surfaces in hyperbolic space of constant mean curvature one. We abbreviate "constant mean curvature one" by CMC-1. These surfaces share many properties with minimal surfaces in R 3 . They possess the "Weierstrass representation" in terms of holomorphic data. This formula was discovered by R. Bryant [1]. Many other properties may be found in papers by M. Umhara and K. Yamada ([4], [5]). Here we try to investigate the hyperbolic analogue of the Gauss map. It is a natural question how the values of the hyperbolic Gauss map distribute. Using Bryant's representation formula we are able to answer this question as follows. Theorem. The hyperbolic Gauss map of nonflat complete CMC-1 surfaces in