minimal disks
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Author(s):  
William H. Meeks ◽  
Giuseppe Tinaglia

AbstractWe describe the lamination limits of sequences of compact disks $$M_n$$ M n embedded in $${\mathbb {R}}^3$$ R 3 with constant mean curvature $$H_n$$ H n , when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi (Ann Math 160:573–615, 2004) for minimal disks. We apply this theorem to prove the existence of a chord arc result for compact disks embedded in $${\mathbb {R}}^3$$ R 3 with constant mean curvature; this chord arc result generalizes Theorem 0.5 by Colding and Minicozzi (Ann Math 167:211–243, 2008) for minimal disks.





2020 ◽  
Vol 116 (2) ◽  
pp. 281-319
Author(s):  
David Hoffman ◽  
Brian White


2020 ◽  
Vol 24 (1) ◽  
pp. 471-532
Author(s):  
Longzhi Lin ◽  
Ao Sun ◽  
Xin Zhou


2016 ◽  
Vol 102 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Jacob Bernstein ◽  
Giuseppe Tinaglia


2015 ◽  
Vol 100 (2) ◽  
pp. 389-394 ◽  
Author(s):  
Brian White
Keyword(s):  
Blow Up ◽  


2014 ◽  
Vol 2015 (17) ◽  
pp. 8268-8274 ◽  
Author(s):  
Ailana Fraser ◽  
Richard Schoen


Author(s):  
Jacob Bernstein ◽  
Christine Breiner
Keyword(s):  


2011 ◽  
Vol 19 (3) ◽  
pp. 487-502 ◽  
Author(s):  
David Hoffman ◽  
Brian White
Keyword(s):  
Blow Up ◽  


2010 ◽  
Vol 62 (6) ◽  
pp. 1264-1275
Author(s):  
Jingyi Chen ◽  
Ailana Fraser

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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