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;
2001-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
