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Explore the mathematical theory of constrained Willmore surfaces in this lecture delivered by Ulrich Pinkall as part of the International Centre for Theoretical Sciences' program on Geometry and Analysis of Minimal Surfaces. Delve into the fundamental concepts and geometric properties of Willmore surfaces, which are critical points of the Willmore functional subject to specific constraints. Learn about the mathematical framework that governs these surfaces and their significance in differential geometry and geometric analysis. Discover how constrained Willmore surfaces relate to minimal surface theory and their applications in various mathematical contexts. This lecture serves as the first installment in a comprehensive series examining the geometric and analytic aspects of these important mathematical objects, providing essential background for understanding advanced topics in minimal surface theory and geometric analysis.
