Geometric Analysis and Topology Seminar

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The cylindrical transform

Speaker: Jake Solomon, Hebrew University

Location: Warren Weaver Hall 517

Date: Wednesday, September 7, 2022, 11 a.m.

Synopsis:

The degenerate special Lagrangian equation (DSL) is a non-linear degenerate elliptic PDE that arises as the geodesic equation for the space of positive Lagrangian submanifolds. Understanding the geodesics of the space of positive Lagrangian submanifolds would shed light on questions ranging from the uniqueness and existence of volume minimizing Lagrangian submanifolds to Arnold's nearby Lagrangian conjecture. I will describe work with A. Yuval on the cylindrical transform, which converts the DSL to a family of non-degenerate elliptic boundary value problems. As a result, we obtain large families of solutions in arbitrary dimension. If time permits, I will discuss some questions about harmonic functions motivated by the cylindrical transform.