We consider hypersurfaces M embedded in a half-space R-+(n+1) with positive constant r(th) symmetric function of the principal curvatures (H_r-surfaces). For such H_r-surfaces, 1 < r less than or equal to n, with strictly convex boundary in the boundary of R(+)(n+1) we show that, if H_r is small enough in terms of the geometry of the boundary of M, then M is topologically a disk. When r = 2, we also prove a compactness theorem for certain classes of H_2-surfaces.

On Hypersurfaces embedded in Euclidean Space with Positive Constant H_r Curvature

NELLI, BARBARA;
2001

Abstract

We consider hypersurfaces M embedded in a half-space R-+(n+1) with positive constant r(th) symmetric function of the principal curvatures (H_r-surfaces). For such H_r-surfaces, 1 < r less than or equal to n, with strictly convex boundary in the boundary of R(+)(n+1) we show that, if H_r is small enough in terms of the geometry of the boundary of M, then M is topologically a disk. When r = 2, we also prove a compactness theorem for certain classes of H_2-surfaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/14412
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