Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2010, Cilt: 3 Sayı: 2, 67 - 101, 30.10.2010

Rafael Lopez

Öz

Kaynakça

  • [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

Yıl 2010, Cilt: 3 Sayı: 2, 67 - 101, 30.10.2010

Rafael Lopez

Öz


Anahtar Kelimeler

mean curvature Maximum Principle Alexandrov theorem balancing formula a priori estimates

Kaynakça

  • [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.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Rafael Lopez

Yayımlanma Tarihi 30 Ekim 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 3 Sayı: 2

Kaynak Göster

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. Ekim 2010;3(2):67-101.
Chicago Lopez, Rafael. “Surfaces With Constant Mean Curvature In Euclidean Space”. International Electronic Journal of Geometry 3, sy. 2 (Ekim 2010): 67-101.
EndNote Lopez R (01 Ekim 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., c. 3, sy. 2, ss. 67–101, 2010.
ISNAD Lopez, Rafael. “Surfaces With Constant Mean Curvature In Euclidean Space”. International Electronic Journal of Geometry 3/2 (Ekim 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, c. 3, sy. 2, 2010, ss. 67-101.
Vancouver Lopez R. Surfaces With Constant Mean Curvature In Euclidean Space. Int. Electron. J. Geom. 2010;3(2):67-101.