Low-carbon economic transformation is a key driver of China's ecological civilization construction， and it is decisive for achieving the goal of carbon peaking and carbon neutrality. In this study， 78 cities in the Yellow River Basin were selected as research objects， and the degree of low-carbon economic transition in the Yellow River Basin from 2010 to 2021 was measured by the entropy weight-TOPSIS method from four dimensions， namely， low-carbon society， low-carbon industry， low-carbon efficiency， and low-carbon environment. Meanwhile， the spatiotemporal pattern， regional differences， and dynamic evolution characteristics were explored deeply by using kernel density， Dagum Gini coefficient， spatial autocorrelation， and spatial Markov chain analyses. The study produced several important results： ① The low-carbon economic transformation in the Yellow River Basin has been improving as a whole， with an average annual growth rate of 4.9%， the spatial distribution of the pattern of 'middle reaches， upstream， and downstream' has been increasing， and there is a polarization phenomenon in the Yellow River Basin and the downstream areas. ② The spatial differences in low-carbon economic transformation are gradually decreasing， with different gaps and trends within and between regions. The hypervariable density is the main source of spatial differences， with an annual average contribution rate of 53.5%. ③ Low-carbon economic transformation is more uneven spatially， with significant positive spatial correlation. Local agglomeration is dominated by high-high agglomeration types， low-low agglomeration phenomena are gradually disappearing， and low-high agglomeration and high-low agglomeration types are diverse and variable. ④ Low-carbon economic transformation is characterized by 'club convergence'， with a clear tendency for upward shifts and a lower likelihood of downward shifts and leapfrogging. In addition， there is a significant spatial spillover effect， which is manifested in the fact that a higher level of neighborhood types is associated with a stronger spatial spillover effect.
Zhang et al. (2025) studied this question.