Monge-Ampère-Gleichungen in der Geometrie SS 2021, Hans-Joachim Hein

Please enroll on LearnWeb before the first meeting.

This seminar is open to students at all levels with an interest in PDEs and Geometric Analysis.

We will meet on Zoom from 12:00-14:00 on Fridays. The first meeting will be on April 16 at 12:00. At this meeting we will discuss some possible topics and assign talks.

Topics: The Monge-Ampère equation is a PDE which prescribes the determinant of the Hessian of an unknown real-valued function. This PDE comes up naturally in a large variety of contexts. The most accessible of these is the geometry of surfaces in R^3: the Gaussian curvature of a graph is essentially given by the Hessian determinant of the graphing function. Two other possible directions for this seminar are optimal transport of probability measures on R^n (Brenier's theorem) and complex geometry (geodesics in the space of Kähler metrics).

Please do not hesitate to contact me (hhein@uni-muenster.de) if you have any questions.