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This course aims to explore recent progress in resolving the log-Minkowski problem and extending results on self-similar solutions in differential geometry. The course covers topics such as Minkowski summation, the Lp Minkowski problem, isotropic and anisotropic cases, uniqueness of solutions, and isomorphic resolution. The teaching method involves presenting theoretical concepts and recent research findings in the field. The course is intended for individuals interested in advanced topics in differential geometry and geometric analysis.