Hamiltonian mean curvature flow

2012/11/05 by Djideme F. Houenou, Houenou, Djideme F., Leonard Todjihounde +1
Mathematics · #53C44 #53D12 #58D05 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53C44 #msc:53D12 #msc:58D05

paper · pdf · doi:10.48550/arxiv.1211.0973

arxiv created 2012/11/05 · arxiv updated 2012/11/06

Abstract

Let (Σ, ω) be a compact Riemann surface with constant curvature c. In this work, we proved that the mean curvature flow of a given Hamiltonian diffeomorphism on Σ provides a smooth path in Ham(Σ), the group of all Hamiltonian diffeomorphisms of Σ. This result gives a proof, in the case of graph of Hamiltonian diffeomorphisms to the conjecture of Thomas and Yau asserting that the mean curvature flow of a compact embedded Lagrangian submanifold S with zero Maslov class in a Calabi- Yau manifolds M exists for all time and converges smoothly to a special Lagrangian submanifold in the Hamiltonian isotopy class of S.

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