Geometric Analysis and Topology Seminar

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Dimension of the singular set of 2-valued stationary graphs

Speaker: Luca Spolaor, UC San Diego

Location: Warren Weaver Hall 512

Date: Friday, May 3, 2024, 11 a.m.

Synopsis:

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.