Minimal hypersurfaces in H × R, total curvature and index
نویسندگان
چکیده
In this paper, we consider minimal hypersurfaces in the product space Hn × R. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the corresponding curvature goes to zero uniformly at infinity. We show that surfaces with finite total intrinsic curvature have finite index. The converse statement is not true as shown by our examples which also serve as useful barriers. MSC(2000): 53C42, 58C40.
منابع مشابه
A ug 2 00 8 Minimal hypersurfaces in H n × R , total curvature and index
In this paper, we consider minimal hypersurfaces in the product space Hn×R. We study the relation between the notions of finite total curvature and index of the stability operator. We study examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations; they serve as counterexamples and are useful barriers for many geometric problems.1
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