Abstract. In this note we establish a generalized Myers theorem under line integral curvature bound for Finsler manifolds.

We investigate complete spacelike hypersurfaces in an Anti-de Sitter space with constant m-th mean curvature and two distinct principal curvatures. By using Otsuki's idea, we obtain some global classification results. For their application, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Anti-de Sitter (n + 1)-spaces (n ≥ 3) of constant mean curvature or constant scalar curvature with two distinct principal curvatures λ and µ satisfying inf(λ − µ) 2 > 0 are the hyperbolic cylinders. It is a little surprising that the corresponding result does not hold for m-th mean curvature when m > 2. We also obtain some global rigidity results for hyperbolic cylinders in terms of square length of the second fundamental form.

Abstract. We first extend the notions of weighted curvatures, including the weighted flag curvature and the weighted Ricci curvature, for a Finsler manifold with given volume form. Then we establish some basic comparison theorems for Finsler manifolds with various weighted curvature bounds. As applications, we obtain some McKean type theorems for the first eigenvalue of Finsler manifolds, some results on weighted curvature and fundamental group for Finsler manifolds, as well as an estimation of Gromov simplicial norms for reversible Finsler manifolds.

We establish a relative volume comparison theorem for minimal volume form of Finsler manifolds under integral Ricci curvature bound. As its applications, we obtain some results on integral Ricci curvature and topology of Finsler manifolds. These results generalize the corresponding properties with pointwise Ricci curvature bound in the literatures.

Biomedical incubation platforms make full use of innovation elements, constantly absorbing, integrating, and allocating various resources and innovating the incubation service mode, an important path to improving the performance of innovation incubation. Based on resource-based theory, network theory, and value chain theory, we proposed the conceptual model and research hypothesis for the relationship between innovation elements, incubation capacity, and innovation incubation performance in biomedical incubation platforms, with customized service as a moderating variable. The empirical results show that innovation elements have a significant positive impact on the improvement and transition of incubation capacity. Incubation capacity has a significant positive impact on innovation incubation performance in biomedical incubation platforms. Customized service plays a significant positive regulatory role between incubation capacity and innovation incubation performance in biomedical incubation platforms.