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Ailana Fraser - On the free boundary variational problem for minimal disks



AILANA FRASER, Courant Institute, New York, New York  10012, USA
On the free boundary variational problem for minimal disks


We will discuss the problem of extremizing the energy (equivalently area) for maps from the unit disk D into a Riemannian manifold Nhaving boundary lying on a specified embedded submanifold M. The critical points of this geometric variational problem are minimal surfaces which meet the submanifold orthogonally along the boundary. We derive a partial Morse theory for this problem in arbitrary dimensions. In addition, we use the geometry to obtain certain lower bounds on the Morse index for such disks.



 

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