Abstract
A new geometric flow describing the motion of quadrature surfaces is introduced. This characterization enables us to study quadrature surfaces through the investigation of the flow. It is proved that the flow is uniquely solvable under the geometric condition that the initial surface has positive mean curvature. As a consequence, a bifurcation criterion for quadrature surfaces is obtained. In fact, we study a generalized flow which includes the geometric flow and the Hele-Shaw flow as special cases.
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