PROPERLY EMBEDDED SURFACES WITH CONSTANT MEAN CURVATURE By ANTONIO ROS and HAROLD ROSENBERG
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چکیده
In this paper we prove a maximum principle at infinity for properly embedded surfaces with constant mean curvature H > 0 in the 3-dimensional Euclidean space. We show that no one of these surfaces can lie in the mean convex side of another properly embedded H surface. We also prove that, under natural assumptions, if the surface lies in the slab |x3| < 1/2H and is symmetric with respect to the plane x3 = 0, then it intersects this plane in a countable union of strictly convex closed curves.
منابع مشابه
Properly embedded surfaces with constant mean curvature
In this paper we prove a maximum principle at infinity for properly embedded surfaces with constant mean curvature H > 0 in the 3-dimensional Euclidean space. We show that no one of these surfaces can lie in the mean convex side of another properly embedded H surface. We also prove that, under natural assumptions, if the surface lies in the slab |x3| < 1/2H and is symmetric with respect to the ...
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تاریخ انتشار 2010