Open AccessMean curvature flow of asymptotically conical Lagrangian submanifolds
Author(s) -
Wei-Bo Su
Publication year - 2019
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/7946
Subject(s) - mathematics , equivariant map , conical surface , lagrangian , mean curvature flow , flow (mathematics) , curvature , convergence (economics) , mathematical analysis , pure mathematics , mean curvature , geometry , economics , economic growth
In this paper, we study Lagrangian mean curvature flow (LMCF) of asymptotically conical (AC) Lagrangian submanifolds asymptotic to a union of special Lagrangian cones. Since these submanifolds are non-compact, we establish a short-time existence theorem for AC LMCF first. Then we focus on the equivariant, almost-calibrated case and prove long-time existence and convergence results. In particular, under certain smallness assumptions on the initial data, we show that the equivariant, almost-calibrated AC LMCF converges to a Lagrangian catenoid or an Anciaux’s expander.