Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.Comment: The result concerning ACyl manifolds was removed from the previous version since it can be generalized and does not depend on either Ricci soliton or Ricci-flat condition. 18 page

How to Measure Carbon Equity: Carbon Gini Index Based on Historical Cumulative Emission Per Capita

This paper uses Lorenz Curve and Gini Index with adjustment to per capita historical cumulative emission and constructs Carbon Gini Index to measure inequality in climate change area. The analysis using Carbon Gini Index shows that 70% of carbon space in the atmosphere has been used for unequal distribution, which is almost the same as that of income in the country with the biggest gap between rich and poor in the world. The carbon equity should be an urgency and priority in the climate agenda. Carbon Gini Index established in this paper can be used to measure inequality in the distribution of carbon space and provide a quantified indicator for measurement of carbon equity among different proposals.Climate Change, Carbon Equity, Long-term Mitigation Goal, Cumulative Emission Per Capita, Carbon Gini Index