Dimension of the singular set of 2-valued stationary graphs

Luca Spolaor, University of California, San Diego
Fine Hall 110

*note location change*

As a consequence of the celebrated Allard’s epsilon regularity theorem, it is well known that the singular set of an integral stationary n-varifold is meager. However, all known examples suggests that the Hausdorff dimension of such singular set should be (n-1). In this talk I will present a recent result, joint with J. Hirsch (Leipzig), where we show that if the stationary varifold is a 2-valued Lipschitz n-graph, then indeed its singular set is of dimension (n-1). I will spend ample time introducing the problem and explaining what are the main difficulties.