This chapter presents the uniqueness of critical point of the solution to the prescribed constant mean curvature equation over convex domain in R2. It explores that it is possible to treat in the unified manner by modifying the method of Chen. Since our theorem concerns only qualitative property of the solution, so only under the hypothesis of the existence of the solution this chapter proves the theorem. In the proof of this theorem it is seen that the level sets of the solution to are convex when H is sufficiently small and Q is strictly convex. This chapter provides several basic lemmas. The first two lemmas are proved by the method based on Chen & Huang's comparison technique.
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