Hypersurfaces of Einstein manifolds

After constructing the initial balanced approximately CMC surface # ˜ (by gluing together small geodesic spheres and catenoidal necks) we seek to perturb this approximate solution

These errors (of the second author) were observed and rectified by James Faran. These changes do not affect any other statements of

The family of the curves so obtained satisfies a system of second order differential equations which is holomorphically invariantly associated with the manifold..

Simons initiated a study of minimal cones from a more differential geometric point of view than had previously been attempted.. One of Simons' main results was an

We also prove a Heintze–Karcher–Ros type inequality for hypersurfaces with free boundary in a ball, which, together with the new Minkowski formula, yields a new proof of

Finally, we use Colding–Minicozzi’s theory of minimal laminations (adapted to the free boundary set- ting) to establish a stronger curvature estimate (Theorem 1.2) for properly

The curvature estimates from Theorem 1.4 ensure that the curvature op- erator is uniformly elliptic, and in view of well-known regularity results we then conclude that the flow

First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of integral of the mean curvature, and with the Gauss-Kronecker curvature