Calculus of Variations and Geometric Measure Theory
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The fractional Liouville equation in dimension 1 - Compactness and quantization

Luca Martinazzi (University of Padua)

created by malchiodi on 08 Jul 2015

14 jul 2015 -- 16:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi Scienze

Abstract.

In this talk I will introduce the fractional Liouville equation on the circle S1 and its geometric interpretation in terms of conformal immersions of the unit disk into the complex plane. Using this interpretation we can show that the solution of the fractional Liouville equation have very precise compactness properties (including quantization) with a clear geometric counterpart. I will also compare these result with analogue ones for the classical Liouville equation in dimension 2, used to prescribe the Gaussian curvature.

This is a joint work with Tristan Riviere and Francesca Da Lio.

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