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Statement of result. A surface in a manifold is called "regular" to emphasize that it is immersed; the term "generalized surface" is used when regularity is only assumed almost everywhere. We treat generalized surfaces of constant mean curvature in an analytic Riemannian manifold Moi dimension 3. To this end consider the variational problem : E[X] = D[X] + 4HV[X] -» min A MS 1970 subject classifications. Primary 49F22, 35B99, 49F25; Secondary 53B20, 49F10.doi:10.1090/s0002-9904-1971-12700-3 fatcat:clab5r22f5cxnc6p2vzgukd6u4