Goal:
The present course gives an introduction to the theory of minimal surfaces.
Some topics that will be covered:
Riemannian metrics, mean curvature of submanifolds
First variation of area/volume
Parametric and nonparametric minimal surfaces, examples
Bernstein's theorem
Weierstrass representation
Omission of the Gauss map
Plateau's problem
Literature:
U. Dierkes, S. Hildebrandt, A. Kuester, O. Wohlrab: Minimal Surfaces, Springer 2010.
J.H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflaechen, Springer 2007.
H. B. Lawson: Lectures on Minimal Submanifolds, Publish or Perish 1980.
J. C. C. Nitsche: Lectures on Minimal Surfaces: Volume 1, Cambridge University Press 2011.
R. Osserman: A survey of Minimal Surfaces, Dover Publications 2002.
