Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Romain Petrides (Université Paris Diderot (Paris 7)
Date:

Thu, 2018-03-15 16:30 - 17:30 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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/4652