6533b853fe1ef96bd12acde1

RESEARCH PRODUCT

Evolution by mean curvature flow of Lagrangian spherical surfaces in complex Euclidean plane

Vicente MiquelAna M. LermaIldefonso Castro

subject

Mathematics - Differential GeometryMean curvature flowApplied Mathematics010102 general mathematicsMathematical analysisTorusClifford torus01 natural sciencessymbols.namesakeDifferential Geometry (math.DG)0103 physical sciencesEuclidean geometrysymbolsFOS: MathematicsPrimary 53C44 53C40 Secondary 53D12010307 mathematical physics0101 mathematicsFinite timeMathematics::Symplectic GeometryAnalysisLagrangianMathematics

description

We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane $\mathbb{C}^2$. In particular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves about finding out a condition on a starting Lagrangian torus in $\mathbb{C}^2$ such that the corresponding mean curvature flow becomes extinct at finite time and converges after rescaling to the Clifford torus.

yearjournalcountryeditionlanguage
2016-03-10
http://arxiv.org/abs/1603.03229