251 research outputs found
The rigidity of embedded constant mean curvature surfaces
We study the rigidity of complete, embedded constant mean curvature surfaces
in R^3. Among other things, we prove that when such a surface has finite genus,
then intrinsic isometries of the surface extend to isometries of R^3 or its
isometry group contains an index two subgroup of isometries that extend.Comment: 10 page
Existence of regular neighborhoods for H-surfaces
In this paper, we study the global geometry of complete, constant mean
curvature hypersurfaces embedded in n-manifolds. More precisely, we give
conditions that imply properness of such surfaces and prove the existence of
fixed size one-sided regular neighborhoods for certain constant mean curvature
hypersurfaces in certain n-manifolds.Comment: 11 page
One-sided curvature estimates for H-disks
In this paper we prove an extrinsic one-sided curvature estimate for disks
embedded in with constant mean curvature which is independent of
the value of the constant mean curvature. We apply this extrinsic one-sided
curvature estimate in [24] to prove to prove a weak chord arc type result for
these disks. In Section 4 we apply this weak chord arc result to obtain an
intrinsic version of the one-sided curvature estimate for disks embedded in
with constant mean curvature. In a natural sense, these
one-sided curvature estimates generalize respectively, the extrinsic and
intrinsic one-sided curvature estimates for minimal disks embedded in
given by Colding and Minicozzi in Theorem 0.2 of [8] and in
Corollary 0.8 of [9].Comment: Minor corrections. References updated. Format change
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