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We provide a new topological obstruction for complete stable minimal hypersurfaces in IR n+1. For n ≥ 3, we prove that a complete orientable stable minimal hypersurface in IR n+1 cannot have more than one end by showing the existence of a bounded harmonic function based on the Sobolev inequality for minimal submanifolds [MS] and by applying the Liouville… (More)

- Tom Ngo, Doug Cutrell, Jenny Dana, Bruce Randall Donald, Lorie Loeb, Shunhui Zhu
- SIGGRAPH
- 2000

O ur goal is to em bed free-form constraints into a graphical m odel. W ith such constraints a graphic can m aintain its visual integrity— and break rules tastefully— while being m anipulated by a casualuser. A typicalparam eterized graphic does notm eet these needs because its configuration space contains nonsense im ages in m uch higher… (More)

- SHUNHUI ZHU
- 1997

We survey comparison results that assume a bound on the man-ifold's Ricci curvature.

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein theorem which says that if the image of the Gauss map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result… (More)

Using the Green's function and some comparison theorems, we obtain a lower bound on the rst Dirichlet eigenvalue for a domain D on a complete manifold with curvature bounded from above. And the lower bound is given explicitly in terms of the diameter of D and the dimension of D. This result can be considered as an analogue for nonpositively curved manifolds… (More)

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