Minimal surfaces in Riemannian manifolds

Summary

The study of minimal surfaces constitutes a central area of research in mathematics, with applications in both geometry and theoretical physics. These beautiful objects have inspired many new areas of research with a particular current focus on understanding the type of minimal surface admitted by a given ambient manifold, coupled with classifying those which are admitted. There are many starting points for a project in this general area, including the related fields of harmonic maps, constant-mean-curvature surfaces, Willmore surfaces, elliptic regularity theory and the spectral analysis of Schroedinger operators on Riemannian manifolds.

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