The Jacobian, the square root and the set ∞

Fabrice Bethuel

(Laboratoire Jacques-Louis LIONs, Université Pierre et Marie Curie, Paris)

Event: ERC Workshop on Existence and Regularity for Nonlinear Systems of Partial Differential Equations

Date: Jun 30, 2014, time: 11:20

Abstract. We discuss the problem of prescribing the Jacobian determinant in dimension two: we restrict ourselves to the case the datum is a finite sum of Dirac masses with integer multiplicity. The main point here is to show that we may relate this problem to the search of harmonic maps into a singular space which is shaped as the symbol ∞ (or the number 8). The later problem in turn is closely linked to meromorphic functions. A large part of the presentation is devoted to a presentation of the various mathematical objets and their connections.