scholarly journals Helicoid-like minimal disks and uniqueness

2011 ◽  
Vol 2011 (655) ◽  
Author(s):  
Jacob Bernstein ◽  
Christine Breiner
Keyword(s):  
Minimal Disks

scholarly journals Embedded minimal disks: Proper versus nonproper—global versus local

2003 ◽  
Vol 356 (1) ◽  
pp. 283-289 ◽  
Author(s):  
Tobias H. Colding ◽  
William P. Minicozzi
Keyword(s):  
Minimal Disks

Singular curves bounding two unstable minimal disks

1999 ◽  
Vol 100 (3) ◽  
pp. 351-373
Author(s):  
Jin Choi
Keyword(s):  
Minimal Disks

scholarly journals Topological type of limit laminations of embedded minimal disks

2016 ◽  
Vol 102 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Jacob Bernstein ◽  
Giuseppe Tinaglia
Keyword(s):  
Topological Type ◽  
Minimal Disks

Holomorphic Variations of Minimal Disks with Boundary on a Lagrangian Surface

2010 ◽  
Vol 62 (6) ◽  
pp. 1264-1275
Author(s):  
Jingyi Chen ◽  
Ailana Fraser
Keyword(s):  
Morse Index ◽  
Kähler Manifold ◽  
Maslov Index ◽  
Minimal Immersion ◽  
Lagrangian Submanifold ◽  
Lagrangian Surface ◽  
Real Dimension ◽  
The Real ◽  
Linearly Independent ◽  
Minimal Disks

AbstractLet L be an oriented Lagrangian submanifold in an n-dimensional Kähler manifold M. Let u: D → M be a minimal immersion from a disk D with u(𝜕D) ⊂ L such that u(D) meets L orthogonally along u(𝜕D). Then the real dimension of the space of admissible holomorphic variations is at least n + μ(E, F), where μ(E, F) is a boundary Maslov index; the minimal disk is holomorphic if there exist n admissible holomorphic variations that are linearly independent over ℝ at some point p ∈ 𝜕D; if M = ℂPn and u intersects L positively, then u is holomorphic if it is stable, and its Morse index is at least n + μ(E, F) if u is unstable.

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