The Impact of Socio-Economic Challenges and Technological Progress on Economic Inequality: An Estimation with the Perelman Model and Ricci Flow Methods

The article examines the impact of 16 key parameters of the Georgian economy on economic inequality, using the Perelman model and Ricci flow mathematical methods. The study aims to conduct a deep analysis of the impact of socio-economic challenges and technological progress on the dynamics of the Gini coefficient. The article examines the following parameters: income distribution, productivity (GDP per hour), unemployment rate, investment rate, inflation rate, migration (net negative), education level, social mobility, trade infrastructure, capital flows, innovative activities, access to healthcare, fiscal policy (budget deficit), international trade (turnover relative to GDP), social protection programs, and technological access. The results of the study confirm that technological innovations and social protection programs have a positive impact on reducing inequality. Productivity growth, improving the quality of education, and strengthening R&D investments increase the possibility of inclusive development. Sensitivity analysis shows that social mobility and infrastructure are important factors that affect economic stability. The accuracy of the model is confirmed by high R^2 values (80-90%) and the statistical reliability of the Z-statistic (<0.05). The study uses Ricci flow methods, which allow for a geometric analysis of the transformation of economic parameters in time and space. Recommendations include the strategic introduction of technological progress, the expansion of social protection programs, improving the quality of education, and encouraging international trade, which will contribute to economic sustainability and reduce inequality. The article highlights multifaceted approaches that combine technological innovation and responses to socio-economic challenges to ensure sustainable and inclusive economic development.