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Explore the intriguing world of isoperimetric problems in this 50-minute lecture by Kateryna Tatarko from the Hausdorff Center for Mathematics. Delve into the classical isoperimetric problem, which demonstrates that the Euclidean ball possesses the largest volume among all convex bodies in Rn with a fixed surface area. Investigate the reverse of this theorem for a specific class of convex bodies, focusing on those with curvature at each point of their boundary bounded below by a positive constant. Examine the challenge of minimizing volume within this class of convex bodies and discover the solution for the three-dimensional case in R3. Gain insights into advanced geometric concepts and their applications in mathematical research.
