),1, 903–906 (1979), Fischer-Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature. Math. Ci.55, 9–10 (1983), Hsiang, W.Y., Teng, Z.H., Yu, W.: New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space. surface is immersed as a constant mean curved surface of a four-dimensional. Surfaces that minimize area under a volume constraint have constant mean curvature (CMC); this condition can be expressed as a nonlinear partial … Secondary 53A10. Master's thesis, IMPA 1982, Frid, H., Thayer, F.J.: The Morse index theorem for elliptic problems with a constraint. J.32, 147–153 (1980), Lawson, B., Jr.: Lectures on Minimal Submanifolds, vol.1. Equations of constant mean curvature surfaces in S 3 and H 3 15. Equations of constant mean curvature surfaces in S 3 and H 3 15. The geometry of the surface of a sphere is the geometry of a surface with constant curvature: the surface of a sphere has the same curvature everywhere. Ann. Now suppose that our surface 5 has constant mean curvature H. Let z = ul + ( — l)ll2u2, complex local coordinate, and define 4>iz) = (611-622) + 2(-l)1'2Z>12. As 2H=bne~x+b22e~x = ibii+b22)e->L is constant, (4.3) says that d/dz = %{d/du1 + i — l)ll2d/du2} annihilates d>', thus
0.We prove that there exists a graph with constant mean curvature H and with boundary ∂Ω if and only if Ω is included in an infinite strip of width 1 H.We also establish an existence result for convex bounded domains contained in a strip. Brasil. To access this article, please, Access everything in the JPASS collection, Download up to 10 article PDFs to save and keep, Download up to 120 article PDFs to save and keep. Download it once and read it on your Kindle device, PC, phones or tablets. mathematical papers. Then ψ has constant mean curvature if and only if it is a critical point of the area functional for any compactly supported variation that preserves the volume enclosed by the surface. Minimal tori in S 3 and Willmore tori 18. Mathematics Subject Classification (2000). Journals Notation. Books In the last case, the second fundament. An. The oldest mathematics journal in the Western Hemisphere in
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