Authors: Marco Rigoli Isabel M C Salavessa
Publish Date: 1993/12/01
Volume: 81, Issue: 1, Pages: 203-222
Abstract
We study Willmore immersed submanifoldsf M m →S n into thenMöbius space withm≥2 as critical points of a conformally invariant functionalW We compute the EulerLagrange equation and relate this functional with another one applied to the conformal Gauss map of immersions intoS n We solve a Bernesteintype problem for compact Willmore hypersurfaces ofS n namely if ∃a ∈ℝn+2 such that γf a ≠ 0 onM whereγ f is the hyperbolic conformal Gauss map and is the Lorentz inner product ofℝn+2 and iff satisfies an additional condition thenfM is an n−1sphere
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