The construction of low-carbon cities is an essential component of sustainable urban development. However, there is a lack of a comprehensive low-carbon city design and evaluation system that incorporates "carbon sink accounting-remote sensing monitoring-numerical modelling-design and application" in an all-around linkage, multi-scale coupling, and localized effects. This paper utilizes the Citespace tool to evaluate low-carbon city design applications by analyzing literature in the Web of Science (WOS) core collection database. The results reveal that low-carbon cities undergo four stages: "measurement-implementation-regulation - management." The research themes are divided into three core clustering evolutionary pathways: "extension of carbon sink functions," "spatialisation of carbon sink systems," and "full-cycle, full-dimensional decarbonisation." Applications include "Utility studies of multi-scale carbon sink assessments," "Correlation analysis of carbon sink influencing factors," "Predictive characterisation of multiple planning scenarios," and "Spatial planning applications of urban sink enhancement." Future low-carbon city construction should incorporate intelligent algorithm technology in real-time to provide a strong design basis for multi-scale urban spatial design with the features of "high-precision accounting, full-cycle assessment and low-energy concept."