Softcover ISBN:  9782856299050 
Product Code:  SMFMEM/161 
List Price:  $52.00 
AMS Member Price:  $41.60 
Softcover ISBN:  9782856299050 
Product Code:  SMFMEM/161 
List Price:  $52.00 
AMS Member Price:  $41.60 

Book DetailsMémoires de la Société Mathématique de FranceVolume: 161; 2019; 100 ppMSC: Primary 52; 53; 39; 47
The authors consider smooth isotropic immersions from the 2dimensional torus into \(\mathbb{R}^{2n}\), for \(n\geq 2\). When \(n=2\) the image of such map is an immersed Lagrangian torus of \(\mathbb{R}^4\). The authors prove that such isotropic immersions can be approximated by arbitrarily \(C^0\)close piecewise linear isotropic maps. If \(n\geq 3\) the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well.
The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, the authors introduce a numerical flow in finite dimension, whose limits provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in \(\mathbb{R}^4\). The DMMF program, which is freely available, is based on the Euler method and shows the evolution equation of discrete surfaces in real time, as a movie.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.

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The authors consider smooth isotropic immersions from the 2dimensional torus into \(\mathbb{R}^{2n}\), for \(n\geq 2\). When \(n=2\) the image of such map is an immersed Lagrangian torus of \(\mathbb{R}^4\). The authors prove that such isotropic immersions can be approximated by arbitrarily \(C^0\)close piecewise linear isotropic maps. If \(n\geq 3\) the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well.
The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, the authors introduce a numerical flow in finite dimension, whose limits provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in \(\mathbb{R}^4\). The DMMF program, which is freely available, is based on the Euler method and shows the evolution equation of discrete surfaces in real time, as a movie.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.