Analysis on Metric Spaces Unit
Analysis on Metric Spaces Unit explores analytic and geometric problems arising in diverse spaces, especially those with no priori smooth structures. Our research focuses on partial differential equations, nonlinear potential theory and geometric function theory on various metric spaces. The tools applied in our research include first-order analysis on PI spaces, viscosity solution theory, sub-Riemannian geometry, nonlinear potential theory, control/game theory, etc. This general framework provides a unified and productive approach to studying problems arising in different fields of mathematics.