TY - JOUR
T1 - Nonexistence of Blow-up Flows for Symplectic and Lagrangian Mean Curvature Flows
AU - Yang , Liuqing
JO - Journal of Partial Differential Equations
VL - 3
SP - 199
EP - 207
PY - 2012
DA - 2012/09
SN - 25
DO - http://doi.org/10.4208/jpde.v25.n3.1
UR - https://global-sci.org/intro/article_detail/jpde/5183.html
KW - Symplectic surface
KW - Lagrangian surface
KW - mean curvature flow
AB - <p>In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ&gt;1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ&gt;max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle.</p>