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We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from ($$\text {n}+1$$ n+1 )-dimensional Euclidean space into a given ($$\text {n}+1$$ n+1 )-dimensional Riemannian manifold which characterizes the existence, stability and dynamics of constant mean curvature submanifolds. This is done in terms of a reduced area function...
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