Can One Perturb the Equatorial Zone on a Sphere with Larger Mean Curvature?

We consider the mean curvature rigidity problem of an equatorial zone on a sphere which is symmetric about the equator with width $2w$. There are two different notions on rigidity, i.e. strong rigidity and local rigidity. We prove that for each kind of these rigidity problems, there exists a critical value such that the rigidity holds true if, and only if, the zone width is smaller than that value. For the rigidity part, we used the tangency principle and a specific lemma (the trap-slice lemma we established before). For the non-rigidity part, we construct the nontrivial perturbations by a gluing procedure called the round-corner lemma using the Delaunay surfaces.Comment: 29 pages, 11 figures. Comments welcom

Impact of Resource-Based Economic Transformation Policy on Sulfur Dioxide Emissions: A Case Study of Shanxi Province

Air pollution, particularly SO2 emission, has become a global problem, seriously threatening the sustainable development and health of mankind. Based on the panel data of 248 prefecture-level cities in China during 2003–2018, this study used the Propensity Score Matching-Difference in Difference (PSM-DID) method within the counterfactual framework to evaluate the treatment effect of the policy made by the National Resource-Based Economic Transformation Comprehensive Supporting Reform Pilot Zone (CRZ) on sulfur dioxide (SO2) emissions. The results show the following. (1) The benchmark regression results demonstrate that the CRZ policy has significantly decreased per capita SO2 emissions (PCSO2) and SO2 emissions per unit of GDP (PGSO2) in the pilot zone, and the placebo test indicates that the evaluation of the policy effect is robust. (2) The dynamic effect test indicates that there is a lag in the effect of the CRZ policy on reducing SO2 emissions. The policy effect of the CRZ policy on PCSO2 and PGSO2 was not obvious in the first stage (2011–2015), the CRZ policy significantly reduced the PCSO2 and PGSO2 in the second stage of policy implementation (2016 and beyond), and the reduction effect of CRZ policy on SO2 emissions is increasing over time. (3) The mechanism analysis shows that optimizing industrial structure, increasing human capital, strengthening technological innovation, and expanding opening to the outside world are the main ways for the CRZ policy to reduce SO2 emissions. The study will help promote SO2 emissions reduction in Shanxi Province, providing a reference for the transformation and development of other resource-based cities in China and the world and contributing to accelerating the achievement of regional emission reduction targets and sustainable development

Impact of Resource-Based Economic Transformation Policy on Sulfur Dioxide Emissions: A Case Study of Shanxi Province

Air pollution, particularly SO2 emission, has become a global problem, seriously threatening the sustainable development and health of mankind. Based on the panel data of 248 prefecture-level cities in China during 2003–2018, this study used the Propensity Score Matching-Difference in Difference (PSM-DID) method within the counterfactual framework to evaluate the treatment effect of the policy made by the National Resource-Based Economic Transformation Comprehensive Supporting Reform Pilot Zone (CRZ) on sulfur dioxide (SO2) emissions. The results show the following. (1) The benchmark regression results demonstrate that the CRZ policy has significantly decreased per capita SO2 emissions (PCSO2) and SO2 emissions per unit of GDP (PGSO2) in the pilot zone, and the placebo test indicates that the evaluation of the policy effect is robust. (2) The dynamic effect test indicates that there is a lag in the effect of the CRZ policy on reducing SO2 emissions. The policy effect of the CRZ policy on PCSO2 and PGSO2 was not obvious in the first stage (2011–2015), the CRZ policy significantly reduced the PCSO2 and PGSO2 in the second stage of policy implementation (2016 and beyond), and the reduction effect of CRZ policy on SO2 emissions is increasing over time. (3) The mechanism analysis shows that optimizing industrial structure, increasing human capital, strengthening technological innovation, and expanding opening to the outside world are the main ways for the CRZ policy to reduce SO2 emissions. The study will help promote SO2 emissions reduction in Shanxi Province, providing a reference for the transformation and development of other resource-based cities in China and the world and contributing to accelerating the achievement of regional emission reduction targets and sustainable development