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On a generalized Calabi-Yau equation

Hongyu Wang, Peng Zhu (2010)

Annales de l’institut Fourier

Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension 2 .

On Schrödinger maps from T 1 to  S 2

Robert L. Jerrard, Didier Smets (2012)

Annales scientifiques de l'École Normale Supérieure

We prove an estimate for the difference of two solutions of the Schrödinger map equation for maps from T 1 to  S 2 . This estimate yields some continuity properties of the flow map for the topology of  L 2 ( T 1 , S 2 ) , provided one takes its quotient by the continuous group action of  T 1 given by translations. We also prove that without taking this quotient, for any t > 0 the flow map at time t is discontinuous as a map from 𝒞 ( T 1 , S 2 ) , equipped with the weak topology of  H 1 / 2 , to the space of distributions ( 𝒞 ( T 1 , 3 ) ) * . The argument relies in an essential...

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