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Min-Max construction for free boundary minimal disks.

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Romain Petrides (Université Paris Diderot (Paris 7)
Thu, 2018-03-15 16:30 - 17:30
MPIM Lecture Hall

We will discuss existence of minimal disks into a Riemannian manifold having a boundary lying on a specified embedded submanifold and that meet the submanifold orthogonally along the boundary. A general existence result has been obtained by A. Fraser. Her construction was inspired by Sacks-Uhlenbeck construction of minimal $2$-spheres : the existence is obtained by a limit procedure for a perturbed energy functional whose critical points are called $\alpha$-harmonic maps. We will explain how it is possible to adapt ideas of Colding-Minicozzi. These ideas go back to the replacement method of Birkhoff for the existence of geodesics. This approach gives  general  energy identities that include bubbles. This is a joint work with P. Laurain.


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