Research Article
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Year 2010, Volume: 3 Issue: 2, 67 - 101, 30.10.2010

Rafael Lopez

Abstract

References

  • [1] Alexandrov, A.D.: Uniqueness theorems for surfaces in the large, V. Vestnik Leningrad Univ., 13, No. 19, A.M.S. (Series 2), 21 (1958), 412–416.
  • [2] Al´ıas, L.J., Lo´pez, R., Palmer, B.: Stable constant mean curvature surfaces with circular boundary, Proc. A.M.S. 127 (1999), 1195–1200.
  • [3] Barbosa, J. L.: Constant mean curvature surfaces bounded by a planar curve, Matematica Contemporanea, 1 (1991), 3–15.
  • [4] Brito, F., Earp, R.: Geometric configurations of constant mean curvature surfaces with planar boundary, An. Acad. Bras. Ci. 63 (1991), 5–19.
  • [5] Brito, F., Earp, R., Meeks III, W. H., Rosenberg, H.: Structure theorems for constant mean curvature surfaces bounded by a planar curve, Indiana Univ. Math. J. 40 (1991), 333–343.
  • [6] Eells, J.: The surfaces of delaunay, Math. Intelligencer, 9 (1987), 53–57.
  • [7] de Gennes P. G., Brochard-Wyart F., Qu´er´e D.: Capillarity and wetting phenomena: drops, bubbles, pearls, waves, Springer Verlag, New York, 2004.
  • [8] Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer Verlag, Berlin, 1983.
  • [9] Heinz, H.: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectificable boundary, Arch. Rat. Mec. Anal. 35 (1969), 249–252.
  • [10] Hildebrandt, S.: On the Plateau problem for surfaces of constant mean curvature, Comm. Pure Appl. Math. 23 (1970), 97–114.
  • [11] Hopf, H.: Differential Geometry in the Large, Lecture Notes in Mathematics, 1000, Springer- Verlag, Berlin, 1983.
  • [12] Isenberg, C.: The Science of Soap Films and Soap Bubbles, Dover, New York, 1992.
  • [13] Kapouleas, N.: Compact constant mean curvature surfaces in Euclidean three-space, J. Diff. Geom. 33 (1991), 683–715.
  • [14] Kenmotsu, K.: Surfaces with constant mean curvature, American Math. Soc., Providence, 2003.
  • [15] Koiso, M.: Symmetry of hypersurfaces of constant mean curvature with symmetric boundary, Math. Z. 191 (1986), 567–574.
  • [16] Koiso, M.: A generalization of Steiner symmetrization for immersed surfaces and its appli- cations, Manuscripta Math. 87 (1995), 311–325.
  • [17] Koiso, M.: The uniqueness for stable surfaces of constant mean curvature with free boundary, Bull Kyoto Univ Educ Ser B. 94 (1999), 1–7.
  • [18] Liu, H.: Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), 141–149.
  • [19] L´opez, R.: Surfaces of constant mean curvature bounded by convex curves, Geom. Dedicata 66 (1997), 255–263.
  • [20] L´opez, R. A note on H-surfaces with boundary, J. Geom. 60 (1997), 80–84.
  • [21] L´opez, R.: Constant mean curvature surfaces with boundary in Euclidean three-space, Tsukuba J. Math., 23 (1999), 27–36.
  • [22] L´opez, R.: Constant mean curvature graphs on unbounded convex domains, J. Diff. Eq., 171 (2001), 54–62.
  • [23] L´opez, R.: Wetting phenomena and constant mean curvature surfaces with boundary, Re- views Math. Physics, 17 (2005), 769–792.
  • [24] L´opez, R.: On uniqueness of graphs with constant mean curvature, J. Math. Kyoto Univ., 46 (2007), 771–787.
  • [25] L´opez, R., Montiel, S.: Constant mean curvature disc with boundary, Proc. Amer. Math. Soc., 123 (1995), 1555–1558.
  • [26] L´opez, R., Montiel, S.: Constant mean curvature surfaces with planar boundary, Duke Math. J., 85 (1996), 583–604.
  • [27] Meeks III, W.: The topology and geometry of embedded surfaces of constant mean curvature, J. Diff. Geom. 30 (1989), 465–503.
  • [28] Oprea, J.: The Mathematics of Soap Films: Explorations with Maple, 2000 American Math. Soc.
  • [29] Osserman, R.: Minimal Surfaces, Dover, 1969.
  • [30] Serrin, J.: On surfaces of constant mean curvature which span a given space curve, Math. Z. 112 (1969), 77–88.
  • [31] Serrin, J.: The problem of Dirichlet for quasilinear elliptics equations with many independent variables, Phil. Trans. Roy. Soc. London A 264 (1969), 413–496.
  • [32] Steffen, K.: Parametric surfaces of prescribed mean curvature, Lectures Note in Math. vol. 1713, 211–265, Springer Verlag, Berlin, 1999.
  • [33] Struwe, M.: Plateau’s Problem and the Calculus of Variations, Mathematical Notes, Prin- centon University Press, Princenton, 1988.
  • [34] Wente, H.C.: Counter example to a conjecture of H. Hopf, Pacific J. Math., 121 (1986), 193–243.

Surfaces With Constant Mean Curvature In Euclidean Space

Year 2010, Volume: 3 Issue: 2, 67 - 101, 30.10.2010

Rafael Lopez

Abstract


Keywords

mean curvature Maximum Principle Alexandrov theorem balancing formula a priori estimates

References

  • [1] Alexandrov, A.D.: Uniqueness theorems for surfaces in the large, V. Vestnik Leningrad Univ., 13, No. 19, A.M.S. (Series 2), 21 (1958), 412–416.
  • [2] Al´ıas, L.J., Lo´pez, R., Palmer, B.: Stable constant mean curvature surfaces with circular boundary, Proc. A.M.S. 127 (1999), 1195–1200.
  • [3] Barbosa, J. L.: Constant mean curvature surfaces bounded by a planar curve, Matematica Contemporanea, 1 (1991), 3–15.
  • [4] Brito, F., Earp, R.: Geometric configurations of constant mean curvature surfaces with planar boundary, An. Acad. Bras. Ci. 63 (1991), 5–19.
  • [5] Brito, F., Earp, R., Meeks III, W. H., Rosenberg, H.: Structure theorems for constant mean curvature surfaces bounded by a planar curve, Indiana Univ. Math. J. 40 (1991), 333–343.
  • [6] Eells, J.: The surfaces of delaunay, Math. Intelligencer, 9 (1987), 53–57.
  • [7] de Gennes P. G., Brochard-Wyart F., Qu´er´e D.: Capillarity and wetting phenomena: drops, bubbles, pearls, waves, Springer Verlag, New York, 2004.
  • [8] Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer Verlag, Berlin, 1983.
  • [9] Heinz, H.: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectificable boundary, Arch. Rat. Mec. Anal. 35 (1969), 249–252.
  • [10] Hildebrandt, S.: On the Plateau problem for surfaces of constant mean curvature, Comm. Pure Appl. Math. 23 (1970), 97–114.
  • [11] Hopf, H.: Differential Geometry in the Large, Lecture Notes in Mathematics, 1000, Springer- Verlag, Berlin, 1983.
  • [12] Isenberg, C.: The Science of Soap Films and Soap Bubbles, Dover, New York, 1992.
  • [13] Kapouleas, N.: Compact constant mean curvature surfaces in Euclidean three-space, J. Diff. Geom. 33 (1991), 683–715.
  • [14] Kenmotsu, K.: Surfaces with constant mean curvature, American Math. Soc., Providence, 2003.
  • [15] Koiso, M.: Symmetry of hypersurfaces of constant mean curvature with symmetric boundary, Math. Z. 191 (1986), 567–574.
  • [16] Koiso, M.: A generalization of Steiner symmetrization for immersed surfaces and its appli- cations, Manuscripta Math. 87 (1995), 311–325.
  • [17] Koiso, M.: The uniqueness for stable surfaces of constant mean curvature with free boundary, Bull Kyoto Univ Educ Ser B. 94 (1999), 1–7.
  • [18] Liu, H.: Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), 141–149.
  • [19] L´opez, R.: Surfaces of constant mean curvature bounded by convex curves, Geom. Dedicata 66 (1997), 255–263.
  • [20] L´opez, R. A note on H-surfaces with boundary, J. Geom. 60 (1997), 80–84.
  • [21] L´opez, R.: Constant mean curvature surfaces with boundary in Euclidean three-space, Tsukuba J. Math., 23 (1999), 27–36.
  • [22] L´opez, R.: Constant mean curvature graphs on unbounded convex domains, J. Diff. Eq., 171 (2001), 54–62.
  • [23] L´opez, R.: Wetting phenomena and constant mean curvature surfaces with boundary, Re- views Math. Physics, 17 (2005), 769–792.
  • [24] L´opez, R.: On uniqueness of graphs with constant mean curvature, J. Math. Kyoto Univ., 46 (2007), 771–787.
  • [25] L´opez, R., Montiel, S.: Constant mean curvature disc with boundary, Proc. Amer. Math. Soc., 123 (1995), 1555–1558.
  • [26] L´opez, R., Montiel, S.: Constant mean curvature surfaces with planar boundary, Duke Math. J., 85 (1996), 583–604.
  • [27] Meeks III, W.: The topology and geometry of embedded surfaces of constant mean curvature, J. Diff. Geom. 30 (1989), 465–503.
  • [28] Oprea, J.: The Mathematics of Soap Films: Explorations with Maple, 2000 American Math. Soc.
  • [29] Osserman, R.: Minimal Surfaces, Dover, 1969.
  • [30] Serrin, J.: On surfaces of constant mean curvature which span a given space curve, Math. Z. 112 (1969), 77–88.
  • [31] Serrin, J.: The problem of Dirichlet for quasilinear elliptics equations with many independent variables, Phil. Trans. Roy. Soc. London A 264 (1969), 413–496.
  • [32] Steffen, K.: Parametric surfaces of prescribed mean curvature, Lectures Note in Math. vol. 1713, 211–265, Springer Verlag, Berlin, 1999.
  • [33] Struwe, M.: Plateau’s Problem and the Calculus of Variations, Mathematical Notes, Prin- centon University Press, Princenton, 1988.
  • [34] Wente, H.C.: Counter example to a conjecture of H. Hopf, Pacific J. Math., 121 (1986), 193–243.
There are 34 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Rafael Lopez

Publication Date October 30, 2010
Published in Issue Year 2010 Volume: 3 Issue: 2

Cite

APA Lopez, R. (2010). Surfaces With Constant Mean Curvature In Euclidean Space. International Electronic Journal of Geometry, 3(2), 67-101.
AMA Lopez R. Surfaces With Constant Mean Curvature In Euclidean Space. Int. Electron. J. Geom. October 2010;3(2):67-101.
Chicago Lopez, Rafael. “Surfaces With Constant Mean Curvature In Euclidean Space”. International Electronic Journal of Geometry 3, no. 2 (October 2010): 67-101.
EndNote Lopez R (October 1, 2010) Surfaces With Constant Mean Curvature In Euclidean Space. International Electronic Journal of Geometry 3 2 67–101.
IEEE R. Lopez, “Surfaces With Constant Mean Curvature In Euclidean Space”, Int. Electron. J. Geom., vol. 3, no. 2, pp. 67–101, 2010.
ISNAD Lopez, Rafael. “Surfaces With Constant Mean Curvature In Euclidean Space”. International Electronic Journal of Geometry 3/2 (October 2010), 67-101.
JAMA Lopez R. Surfaces With Constant Mean Curvature In Euclidean Space. Int. Electron. J. Geom. 2010;3:67–101.
MLA Lopez, Rafael. “Surfaces With Constant Mean Curvature In Euclidean Space”. International Electronic Journal of Geometry, vol. 3, no. 2, 2010, pp. 67-101.
Vancouver Lopez R. Surfaces With Constant Mean Curvature In Euclidean Space. Int. Electron. J. Geom. 2010;3(2):67-101.