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Volumn 9, Issue 3, 2007, Pages 355-365

Stable periodic constant mean curvature surfaces and mesoscopic phase separation

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EID: 35648960188     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/168     Document Type: Article
Times cited : (20)

References (30)
  • 1
    • 35648998228 scopus 로고    scopus 로고
    • ALEKSANDROV, A. D. Uniqueness theorems for surfaces in the large I. Vestnik Leningrad. Univ. 11 (1956), 5-17 (in Russian). MR 0086338
    • ALEKSANDROV, A. D. Uniqueness theorems for surfaces in the large I. Vestnik Leningrad. Univ. 11 (1956), 5-17 (in Russian). MR 0086338
  • 3
    • 0024057538 scopus 로고
    • Periodic area-minimizing surfaces in block copolymers
    • ANDERSON, D. M., HOFFMAN, D., HENKEE, C. S., & THOMAS, E. L. Periodic area-minimizing surfaces in block copolymers. Nature 334 (1988), 598-602.
    • (1988) Nature , vol.334 , pp. 598-602
    • ANDERSON, D.M.1    HOFFMAN, D.2    HENKEE, C.S.3    THOMAS, E.L.4
  • 4
    • 0000142915 scopus 로고
    • Stability of hypersurfaces with constant mean curvature
    • Zbl 0513.53002 MR 0735120
    • BARBOSA, J. L., & DO CARMO, M. Stability of hypersurfaces with constant mean curvature. Math. Z. 185 (1984), 339-353. Zbl 0513.53002 MR 0735120
    • (1984) Math. Z , vol.185 , pp. 339-353
    • BARBOSA, J.L.1    DO CARMO, M.2
  • 5
    • 33750002269 scopus 로고    scopus 로고
    • Periodic phase separation: The periodic isoperimetric and Cahn-Hilliard problems
    • Zbl 1109.35092 MR 2273234
    • CHOKSI, R., & STERNBERG, P. Periodic phase separation: the periodic isoperimetric and Cahn-Hilliard problems. Interfaces Free Bound. 8 (2006), 371-392. Zbl 1109.35092 MR 2273234
    • (2006) Interfaces Free Bound , vol.8 , pp. 371-392
    • CHOKSI, R.1    STERNBERG, P.2
  • 6
    • 38249011669 scopus 로고
    • Majoration de la seconde valeur propre d'un opérateur de Schrödinger sur une variété compacte et applications
    • Zbl 0766.58055 MR 1151550
    • EL SOUFI, A., & ILIAS, S. Majoration de la seconde valeur propre d'un opérateur de Schrödinger sur une variété compacte et applications. J. Funct. Anal. 103 (1992), 294-316. Zbl 0766.58055 MR 1151550
    • (1992) J. Funct. Anal , vol.103 , pp. 294-316
    • EL SOUFI, A.1    ILIAS, S.2
  • 7
    • 0002246356 scopus 로고
    • On the regularity of boundaries of sets minimizing perimeter with a volume constraint
    • Zbl 0486.49024 MR 0684753
    • GONZALEZ, E., MASSARI, U., & TAMANINI, I. On the regularity of boundaries of sets minimizing perimeter with a volume constraint. Indiana Univ. Math. J. 32 (1983), 25-37. Zbl 0486.49024 MR 0684753
    • (1983) Indiana Univ. Math. J , vol.32 , pp. 25-37
    • GONZALEZ, E.1    MASSARI, U.2    TAMANINI, I.3
  • 8
    • 35648966837 scopus 로고    scopus 로고
    • GROSSE-BRAUCKMANN, K. Cousins of constant mean curvature surfaces. Global Theory of Minimal Surfaces, Clay Math. Proc. 2, Amer. Math. Soc., Providence, RI (2005), 747-767. Zbl 1110.53041 MR 2167287
    • GROSSE-BRAUCKMANN, K. Cousins of constant mean curvature surfaces. Global Theory of Minimal Surfaces, Clay Math. Proc. 2, Amer. Math. Soc., Providence, RI (2005), 747-767. Zbl 1110.53041 MR 2167287
  • 9
    • 2142834706 scopus 로고    scopus 로고
    • The periodic isoperimetric problem
    • Zbl 1046.52002 MR 2031051
    • HAUSWIRTH, L., PÉREZ, J., ROMON, P., & ROS, A. The periodic isoperimetric problem. Trans. Amer. Math. Soc. 356 (2003), 2025-2047. Zbl 1046.52002 MR 2031051
    • (2003) Trans. Amer. Math. Soc , vol.356 , pp. 2025-2047
    • HAUSWIRTH, L.1    PÉREZ, J.2    ROMON, P.3    ROS, A.4
  • 10
    • 0001005571 scopus 로고
    • Quatre propriétés isopé rimétriques des membranes sphériques homogènes
    • Zbl 0224.73083 MR 0292357
    • HERSCH, J. Quatre propriétés isopé rimétriques des membranes sphériques homogènes. C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1645-A1648. Zbl 0224.73083 MR 0292357
    • (1970) C. R. Acad. Sci. Paris Sér. A-B , vol.270
    • HERSCH, J.1
  • 11
    • 0000785828 scopus 로고
    • 3
    • Zbl 0205.52001 MR 0270280
    • 3. Ann. of Math. 92 (1970), 335-374. Zbl 0205.52001 MR 0270280
    • (1970) Ann. of Math , vol.92 , pp. 335-374
    • LAWSON, H.B.1
  • 12
    • 0035846811 scopus 로고    scopus 로고
    • Perforated wetting layers from periodic patterns of lyophobic surface domains
    • LENZ, P., BECHINGER, C., SCHÄFLE, C., LEIDERER, P., & LIPOWSKY, R. Perforated wetting layers from periodic patterns of lyophobic surface domains. Langmuir 17 (2001), 7814-7822.
    • (2001) Langmuir , vol.17 , pp. 7814-7822
    • LENZ, P.1    BECHINGER, C.2    SCHÄFLE, C.3    LEIDERER, P.4    LIPOWSKY, R.5
  • 13
    • 0037148414 scopus 로고    scopus 로고
    • The standard Gaussian model for block copolymer melts
    • MATSEN, M. W. The standard Gaussian model for block copolymer melts. J. Phys.: Condens. Matter 14 (2002), R21-R47.
    • (2002) J. Phys.: Condens. Matter , vol.14
    • MATSEN, M.W.1
  • 14
    • 1842690836 scopus 로고
    • Lectures on Plateau's problem
    • Universidade Federal do Ceará Brazil
    • MEEKS III, W. H. Lectures on Plateau's problem. Scola de Geometria Diferencial, Universidade Federal do Ceará (Brazil) (1978).
    • (1978) Scola de Geometria Diferencial
    • MEEKS III, W.H.1
  • 15
    • 0344928071 scopus 로고    scopus 로고
    • Regularity of isoperimetric hypersurfaces in Riemannian manifolds
    • Zbl 1063.49031 MR 1997594
    • MORGAN, F. Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Trans. Amer. Math. Soc. 355 (2003), 5041-5052. Zbl 1063.49031 MR 1997594
    • (2003) Trans. Amer. Math. Soc , vol.355 , pp. 5041-5052
    • MORGAN, F.1
  • 16
    • 51249173862 scopus 로고
    • Index and stability of harmonic Gauss maps
    • Zbl 0727.58011 MR 1100840
    • PALMER, B. Index and stability of harmonic Gauss maps. Math. Z. 206 (1991), 563-566. Zbl 0727.58011 MR 1100840
    • (1991) Math. Z , vol.206 , pp. 563-566
    • PALMER, B.1
  • 17
    • 8644246741 scopus 로고    scopus 로고
    • The isoperimetric problem in spherical cylinders
    • Zbl 1082.53066 MR 2103404
    • PEDROSA, R. The isoperimetric problem in spherical cylinders. Ann. Global Anal. Geom. 26 (2004), 333-354. Zbl 1082.53066 MR 2103404
    • (2004) Ann. Global Anal. Geom , vol.26 , pp. 333-354
    • PEDROSA, R.1
  • 19
    • 0002222804 scopus 로고    scopus 로고
    • Index one minimal surfaces in flat three-space forms
    • Zbl 0922.53022 MR 1631568
    • RITORÉ, M. Index one minimal surfaces in flat three-space forms. Indiana Univ. Math. J. 46 (1997), 1137-1153. Zbl 0922.53022 MR 1631568
    • (1997) Indiana Univ. Math. J , vol.46 , pp. 1137-1153
    • RITORÉ, M.1
  • 20
    • 51249163412 scopus 로고
    • Stable constant mean curvature tori and the isoperimetric problem in three space forms
    • Zbl 0760.53037 MR 1161286
    • RITORÉ, M., & ROS, A. Stable constant mean curvature tori and the isoperimetric problem in three space forms. Comment. Math. Helv. 67 (1992), 293-305. Zbl 0760.53037 MR 1161286
    • (1992) Comment. Math. Helv , vol.67 , pp. 293-305
    • RITORÉ, M.1    ROS, A.2
  • 21
    • 21844487214 scopus 로고    scopus 로고
    • The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds
    • Zbl 0867.53007 MR 1322955
    • RITORÉ, M., & ROS, A. The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds. Trans. Amer. Math. Soc. 348 (1996), 391-410. Zbl 0867.53007 MR 1322955
    • (1996) Trans. Amer. Math. Soc , vol.348 , pp. 391-410
    • RITORÉ, M.1    ROS, A.2
  • 22
    • 35648946589 scopus 로고    scopus 로고
    • Personal communication
    • ROMON, P. Personal communication.
    • ROMON, P.1
  • 23
    • 35648948140 scopus 로고    scopus 로고
    • ROS, A. The isoperimetric problem. Global Theory of Minimal Surfaces, Clay Math. Proc. 2, Amer. Math. Soc., Providence, RI (2005), 175-209. Zbl pre05052283 MR 2167260
    • ROS, A. The isoperimetric problem. Global Theory of Minimal Surfaces, Clay Math. Proc. 2, Amer. Math. Soc., Providence, RI (2005), 175-209. Zbl pre05052283 MR 2167260
  • 24
    • 1842662480 scopus 로고    scopus 로고
    • Isoperimetric inequalities in crystallography
    • Zbl 1048.53006 MR 2051615
    • ROS, A. Isoperimetric inequalities in crystallography. J. Amer. Math. Soc. 17 (2004), 373-388. Zbl 1048.53006 MR 2051615
    • (2004) J. Amer. Math. Soc , vol.17 , pp. 373-388
    • ROS, A.1
  • 25
    • 33749389042 scopus 로고    scopus 로고
    • One-sided complete stable minimal surfaces
    • Zbl 1110.53009 MR 2260928
    • ROS, A. One-sided complete stable minimal surfaces. J. Differential Geom. 74 (2006), 69-92. Zbl 1110.53009 MR 2260928
    • (2006) J. Differential Geom , vol.74 , pp. 69-92
    • ROS, A.1
  • 26
    • 11044238498 scopus 로고    scopus 로고
    • Properly embedded surfaces with constant mean curvature
    • Preprint
    • ROS, A., & ROSENBERG, H. Properly embedded surfaces with constant mean curvature. Preprint.
    • ROS, A.1    ROSENBERG, H.2
  • 27
    • 0000049028 scopus 로고
    • P and D surfaces are stable
    • Zbl 0747.53010 MR 1245555
    • ROSS, M. Schwarz' P and D surfaces are stable. Differential Geom. Appl. 2 (1992), 179-195. Zbl 0747.53010 MR 1245555
    • (1992) Differential Geom. Appl , vol.2 , pp. 179-195
    • ROSS, M.S.1
  • 28
    • 0000197823 scopus 로고
    • Inequalities for certain eigenvalues of a membrane of given area
    • Zbl 0055.08802 MR 0061749
    • SZEGÖ, G. Inequalities for certain eigenvalues of a membrane of given area. J. Rational Mech. Anal. 3 (1954), 343-356. Zbl 0055.08802 MR 0061749
    • (1954) J. Rational Mech. Anal , vol.3 , pp. 343-356
    • SZEGÖ, G.1
  • 29
    • 0001991729 scopus 로고
    • Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds
    • Zbl 0446.58017 MR 0577325
    • YANG, P., & YAU, S. T. Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), 55-63. Zbl 0446.58017 MR 0577325
    • (1980) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.7 , pp. 55-63
    • YANG, P.1    YAU, S.T.2
  • 30
    • 0000493117 scopus 로고
    • Nonlinear analysis in geometry
    • Zbl 0631.53002 MR 0896385
    • YAU, S. T. Nonlinear analysis in geometry. Enseign. Math. 33 (1987), 109-158. Zbl 0631.53002 MR 0896385
    • (1987) Enseign. Math , vol.33 , pp. 109-158
    • YAU, S.T.1


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