Seminar Analysis: Petru Mironescu (University Lyon 1)

The structure of complex unimodular maps

We describe the structure of maps u:(0,1)ⁿ → S¹ having a given Sobolev regularity. Such maps are described by their singularities and phases. This is the analog of the Weierstrass factorization theorem for holomorphic functions; the singularities of the Sobolev maps play the role of the zeroes of holomorphic maps. We will present implications of this result to functional analytic questions related to manifold valued maps. If the time permits it, we will discuss the question of the control of the phases, and present some applications to some model PDEs and nonlocal problems.

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