Singularities of lagrangian mean curvature flow: monotone case

• Autores: André Neves
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 1, 2010, págs. 109-126
• Idioma: inglés
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• Resumen

  • We study the formation of singularities for the mean curvature flow of monotone Lagrangians in $\C^n$. More precisely, we show that if singularities happen before a critical time then the tangent flow can be decomposed into a finite union of area-minimizing Lagrangian cones (Slag cones). When $n=2$, we can improve this result by showing that each connected components of the rescaled flow converge to an area-minimizing cone, as opposed to possible non-area minimizing union of Slag cones. In the last section, we give specific examples for which such singularity formation occurs.