Enclosure theorems for generalized mean curvature flows

2003 ◽  
Vol 16 (4) ◽  
pp. 439-447 ◽  
Author(s):  
Sven Winklmann
Keyword(s):  
Mean Curvature ◽  
Generalized Mean Curvature ◽  
Generalized Mean

Motion of level sets by a generalized mean curvature

2002 ◽  
Vol 23 (11) ◽  
pp. 1310-1318
Author(s):  
Zheng Yong-ai ◽  
Liu Zu-han
Keyword(s):  
Mean Curvature ◽  
Level Sets ◽  
Generalized Mean Curvature ◽  
Generalized Mean

scholarly journals Generalized Lagrangian mean curvature flows: The cotangent bundle case

2019 ◽  
Vol 2019 (750) ◽  
pp. 97-121 ◽  
Author(s):  
Knut Smoczyk ◽  
Mao-Pei Tsui ◽  
Mu-Tao Wang
Keyword(s):  
Mean Curvature ◽  
Cotangent Bundle ◽  
Curvature Vector ◽  
Lagrangian Submanifold ◽  
Mean Curvature Vector ◽  
Long Time Existence ◽  
Almost Kähler Manifold ◽  
Generalized Mean Curvature ◽  
Generalized Mean ◽  
Time Existence

Abstract In [18], we defined a generalized mean curvature vector field on any almost Lagrangian submanifold with respect to a torsion connection on an almost Kähler manifold. The short time existence of the corresponding parabolic flow was established. In addition, it was shown that the flow preserves the Lagrangian condition as long as the connection satisfies an Einstein condition. In this article, we show that the canonical connection on the cotangent bundle of any Riemannian manifold is an Einstein connection (in fact, Ricci flat). The generalized mean curvature vector on any Lagrangian submanifold is related to the Lagrangian angle defined by the phase of a parallel {(n,0)} -form, just like the Calabi–Yau case. We also show that the corresponding Lagrangian mean curvature flow in cotangent bundles preserves the exactness and the zero Maslov class conditions. At the end, we prove a long time existence and convergence result to demonstrate the stability of the zero section of the cotangent bundle of spheres.

On the generalized mean curvature

2010 ◽  
Vol 39 (3-4) ◽  
pp. 491-523 ◽  
Author(s):  
Elisabetta Barozzi ◽  
Eduardo Gonzalez ◽  
Umberto Massari
Keyword(s):  
Mean Curvature ◽  
Generalized Mean Curvature ◽  
Generalized Mean
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