Title:
Recent Developments in Classical Minimal Surface Theory
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Abstract:
A minimal submanifold of a fixed Riemannian manifold is a (possibly singular) submanifold which is a critical point for the area functional.  Minimal submanifolds are a fundamental tool in geometry and admit a beautiful and rich theory. In this talk we focus on the classical setting of smooth minimal surfaces in R^3. In particular, we discuss some recent classification results for complete embedded examples.  We  also draw a connection between the classification problem and compactness properties of the space of minimal surfaces.