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Isoperimetric inequality in warped product manifold.

Abstract: We consider isoperimetric inequality in warped product manifold. We discuss two results by Montiel and Bray-Morgan.聽The paper by Montiel shows that under natural assumption of the warped function, a star shaped constant mean curvature聽hypersurface must be a coordinate slice. The paper by Bray-Morgan shows that under stronger assumption of the warped function, isoperimetric domain must be a coordinate slice.