In the global trend of urban shrinkage, urban vitality, as one of the important representations of high-quality urban development, has become a breakthrough. More and more scholars advocate to awaken urban vitality, so as to realize the high-quality development of shrinking cities. This paper takes the municipal districts of 34 cities in the three northeastern provinces of China as study areas, based on the broad concept of urban shrinkage, selects the indicators of population, economy and society, and uses the "two-step diagnostic method" which is consistent with Chinese conditions to identify the urban shrinkage from 2010 to 2018. In this research, the indexes of economic, social, cultural, environmental and spatial dimensions are selected, and the urban vitality and the vitality of each dimension from 2010 to 2018 are calculated and analyzed by using the entropy weight method (EWM). Then, this paper analyzes the correlation between urban shrinkage and urban vitality by Pearson correlation coefficient. The results show that: (1) urban shrinkage in the three northeastern provinces of China has become a regional remarkable phenomenon, which is also an inevitable process in some regions of China and even the world; (2) overall, the urban vitality of cities in the three northeastern provinces of China is steady and rising a little, and there is an obvious spatial agglomeration pattern like "central city polarization"; (3) there is a significant correlation between urban shrinkage and urban vitality, that is, the lower the degree of urban shrinkage, the higher the urban vitality, showing the opposite trend in the process of urban development; (4) the influence of urban shrinkage on each dimension of urban vitality is different, and the correlation results are different, too. In the planning process of shrinking cities in the future, paying attention to the relationship between urban vitality and urban shrinkage, conducting benign guidance on this basis, and adjusting urban vitality elements of different dimensions to stimulate urban development power can enhance urban competitiveness and achieve better development.
Keywords: correlation analysis; shrinking cities; the three northeastern provinces of China; two-step diagnostic method; urban shrinkage; urban vitality.