New Complex Analytic Methods in the Theory of Minimal Surfaces - Franc Forstnerič

Explore recent developments in the theory of minimal surfaces in Euclidean spaces through a comprehensive lecture that applies both classical and modern complex analytic methods. Delve into the global theory of minimal surfaces, covering topics such as the Calabi-Yau problem, constructions of properly immersed and embedded minimal surfaces in R^n and minimally convex domains, complex Gauss map results, and isotopies of conformal minimal immersions. Learn about key concepts including Lagrange's equation, mean curvature function, Plateau problem, Riemann surfaces, and complex analysis. Examine the Rhombus Theorem, proper maps, minimal convexity, and the Riemann-Hilbert boundary value problem. Gain insights from speaker Franc Forstnerič of the University of Ljubljana in this one-hour talk presented by ICTP Mathematics.

Introduction
The concept of minimal surfaces
Lagranges equation
Mean curvature function
Hell equate
Plateau problem
Remains minimal examples
Riemann surfaces
Complex analysis
Upshot
Orca theory
Dual curves
Conjugation minimal surfaces
Websters formula
Topics
Rhombus Theorem
Proof
Lemma
convex hull
Proper maps
Minimal strip
Minimal convexity
Riemann Hilbert boundary value
Complete minimal surfaces
Gauss map