Abstract
We prove a unique continuation theorem for non-minimal biharmonic hypersurfaces of spheres, based on Aronszajn’s 1957 article. Under the right hypotheses, this result shows that, for these immersions, CMC on an open subset implies globally CMC. We then deduce new rigidity theorems to support the Conjecture that biharmonic submanifolds of Euclidean spheres must be of constant mean curvature.
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