Minmax minimal surfaces in arbitrary codimension with

Rivière 2019 01 29

Tristan Rivière
ETH Zürich; Member, School of Mathematics
January 29, 2019

We shall present a procedure which to any admissible family
of immersions
of surfaces into an arbitrary closed riemannian manifolds assigns a
smooth, possibly branched, minimal surface
whose area is equal to the width of the corresponding minmax and whose
Morse index is bounded by the
dimension of the familly. We will discuss the question of bounding the
Morse index + Nullity from below as well as possible extensions of
this procedure to more general families.