Weakly complex Einstein-Finsler vector bundle Dedicated to Professor Tongde Zhong for His 90th Birthday

Let(E, F) be a complex Finsler vector bundle over a compact Khler manifold(M, g) with Khler form Φ. We prove that if(E, F) is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou(1997),then it is modeled on a complex Minkowski space. Consequently, a complex Einstein-Finsler vector bundle(E, F) over a compact Khler manifold(M, g) is necessarily Φ-semistable and(E, F) =(E_1, F_1)⊕…⊕(E_k, F_k),where Fj := F |Ej, and each(Ej, Fj) is modeled on a complex Minkowski space whose associated Hermitian vector bundle is a Φ-stable Einstein-Hermitian vector bundle with the same factor c as(E, F).

交通可达性的提高是否加剧了中国跨省河流污染?——来自中国工业企业的证据

本文选取位于中国七大水系主要河流沿岸的边界县,结合中国工业企业数据库,研究交通可达性的提高对跨省河流沿岸高污染企业生产活动带来的影响。研究发现:(1)交通可达性的提高促进了高污染企业的生产活动向上游省的下游边界县集中,而对清洁企业的影响不显著;(2)交通可达性的提高所带来的中国跨省河流污染主要是因上游省边界县现有污染企业的扩大再生产引起的;(3)交通可达性的提高对上游省边界县国有污染企业生产活动的影响最大,私营和外资企业受到的影响较小。

On Unitary Invariant Weakly Complex Berwald Metrics with Vanishing Holomorphic Curvature and Closed Geodesics

In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M  C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.

Strongly convex weakly complex Berwald metrics and real Landsberg metrics

Under the assumption that' is a strongly convex weakly Khler Finsler metric on a complex manifold M, we prove that F is a weakly complex Berwald metric if and only if F is a real Landsberg metric.This result together with Zhong(2011) implies that among the strongly convex weakly Kahler Finsler metrics there does not exist unicorn metric in the sense of Bao(2007). We also give an explicit example of strongly convex Kahler Finsler metric which is simultaneously a complex Berwald metric, a complex Landsberg metric,a real Berwald metric, and a real Landsberg metric.

On U(n)-invariant strongly convex complex Finsler metrics

In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between real and complex Finsler geometries via concrete and computable examples.We prove a rigid theorem which states that a U(n)-invariant strongly convex complex Finsler metric F is a real Berwald metric if and only if F comes from a U(n)-invariant Hermitian metric.We give a characterization of U(n)-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of the U(n)-invariant strongly pseudoconvex complex Finsler metric.Finally,we prove that the real geodesics of some U(n)-invariant complex Finsler metric restricted on the unit sphere S^(2n-1)■C^(n) share a specific property as that of the complex Wrona metric on C^(n).

A class of metrics and foliations on tangent bundle of Finsler manifolds

让(M， F ) 是 Finsler 歧管，并且让 TM 0 是有概括 Riemannian 公制的 G 的 M 的裂缝正切捆，它被 F 导致。在这份报纸，我们提取许多自然生叶(TM 0,G) 和学习他们的几何性质。下次，我们使用这条途径与积极经常的旗帜弯曲获得 Finsler manifolds 的新描述。我们也调查在 Levi-Civita 连接， Cartan 连接， Vaisman 连接，垂直生叶，和 Reinhart 空格之间的关系。

Schwarz lemma from a Kähler manifold into a complex Finsler manifold

Suppose that M is a complete Kähler manifold such that its holomorphic sectional curvature is bounded from below by a constant and its radial sectional curvature is also bounded from below.Suppose that N is a strongly pseudoconvex complex Finsler manifold such that its holomorphic sectional curvature is bounded from above by a negative constant.In this paper,we establish a Schwarz lemma for holomorphic mappings f from M into N.As applications,we obtain a Liouville type rigidity result for holomorphic mappings f from M into N,as well as a rigidity theorem for bimeromorphic mappings from a compact complex manifold into a compact complex Finsler manifold.

China’s Government Information Capacity,Medical Resource Allocation and COVID−19 Prevention and Control

The fight against the COVID−19 epidemic is a war against an“invisible enemy”.Access to accurate information and appropriate allocation of medical resources are key to containing the spread of the virus as soon as possible.The Chinese government has great power to collect information from individuals and basic-level organizations.It also has strong ability to pool and allocate medical resources.The fight against COVID−19 can be deemed as a quasi-natural experiment and based on this,we examine how government information capacity and medical resource allocation influence epidemic prevention and control in 286 Chinese cities(prefecture level and above).The fi ndings are as follows:(1)Government information capacities improve the effectiveness of prevention and control policies.At city level,for every 0.1 point of increase in government information capacity score,the number of confi rmed cases will reduce by 66.5,and the number of deaths per 10000 people will be down by 0.008.(2)The quantity of medical resources available has no direct influence on the effectiveness of epidemic prevention and control,but higher allocation efficiency does bring higher effectiveness.(3)The government can,on the one hand,allocate public resources based on information,and on the other hand guide the flow of social resources by releasing relevant information.Both can improve the allocation efficiency of medical resources.These fi ndings have some policy implications for improving global emergency management.