The CMC Dynamics Theorem in R^3

Meeks, William H. and Tinaglia, Giuseppe (2008) The CMC Dynamics Theorem in R^3. [Preprint]
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In this paper, we develop some new tools and theory that are useful in describing the geometry of properly embedded, constant mean curvature surfaces in R^3 with bounded second fundamental form. More precisely, we prove dynamics type results for the space of translational limits of such a surface. As a consequence of our main theorems, in subsequent papers we obtain rigidity results for certain properly embedded, constant mean curvature surfaces in R^3, as well as derive curvature estimates for complete, embedded, constant mean curvature surfaces in complete locally homogeneous three- manifolds.

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Meeks, William H.
Tinaglia, Giuseppe
Deposit date
27 Mar 2008
Last modified
16 May 2011 12:07

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