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Volumn 17, Issue 2, 2004, Pages 373-388

Isoperimetric inequalities in crystallography

Author keywords

Cubic symmetry; Isoperimetric problem; Periodic minimal surfaces

Indexed keywords


EID: 1842662480     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-03-00447-8     Document Type: Article
Times cited : (11)

References (30)
  • 1
    • 0002019195 scopus 로고
    • Uniqueness theorems for surfaces in the large I
    • MR 19:167c
    • A. D. Alexandrov, Uniqueness theorems for surfaces in the large I, Vestnik Leningrad Univ. Math. 11 (1956), 5-17. MR 19:167c
    • (1956) Vestnik Leningrad Univ. Math. , vol.11 , pp. 5-17
    • Alexandrov, A.D.1
  • 3
    • 0000910006 scopus 로고
    • Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
    • MR 54:8420
    • F. J. Almgren, Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. AMS 165 (1976). MR 54:8420
    • (1976) Mem. AMS , vol.165
    • Almgren, F.J.1
  • 5
    • 0002794081 scopus 로고
    • Geometric orbifolds
    • MR 90k:22011
    • W. D. Dunbar Geometric orbifolds, Rev. Mat. Univ. Complu. 1 (1988) 67-99. MR 90k:22011
    • (1988) Rev. Mat. Univ. Complu. , vol.1 , pp. 67-99
    • Dunbar, W.D.1
  • 6
    • 3043002716 scopus 로고    scopus 로고
    • Spanning minimal surfaces
    • MR 97i:53009
    • W. Fischer and E. Koch Spanning minimal surfaces, Phil. Trans. R. Soc. Lond. A354(1996), 2105-2142. MR 97i:53009
    • (1996) Phil. Trans. R. Soc. Lond. , vol.A354 , pp. 2105-2142
    • Fischer, W.1    Koch, E.2
  • 7
    • 0001591862 scopus 로고    scopus 로고
    • Exact computation of the triply periodic G (Gyroid) minimal surface
    • P. J. F. Gandy and J. Klinowski, Exact computation of the triply periodic G (Gyroid) minimal surface, Chem. Phys. Lett. 321 (2000), 363-371.
    • (2000) Chem. Phys. Lett. , vol.321 , pp. 363-371
    • Gandy, P.J.F.1    Klinowski, J.2
  • 8
    • 0002246356 scopus 로고
    • On the regularity of boundaries of sets minimizing perimeter with a volume constraint
    • MR 84d:49043
    • E. Gonzalez, U. Massari, and I. Tamanini, On the regularity of boundaries of sets minimizing perimeter with a volume constraint, Indiana Univ. Math. J. 32 (1983), 25-37. MR 84d:49043
    • (1983) Indiana Univ. Math. J. , vol.32 , pp. 25-37
    • Gonzalez, E.1    Massari, U.2    Tamanini, I.3
  • 9
    • 0031537321 scopus 로고    scopus 로고
    • Gyroids of Constant Mean Curvature
    • MR 98i:53013
    • K. Grosse-Brauckmann, Gyroids of Constant Mean Curvature, Exp. Math. 6 (1997), 21-38. MR 98i:53013
    • (1997) Exp. Math. , vol.6 , pp. 21-38
    • Grosse-Brauckmann, K.1
  • 10
    • 0001031874 scopus 로고
    • Gitterperiodische Punktmengen und Isoperimetrie
    • MR 48:2902
    • H. Hadwiger, Gitterperiodische Punktmengen und Isoperimetrie, Monatsh. Math. 76 (1972) 410-418. MR 48:2902
    • (1972) Monatsh. Math. , vol.76 , pp. 410-418
    • Hadwiger, H.1
  • 13
    • 0038276386 scopus 로고    scopus 로고
    • Identification of lyotropic liquid crystalline mesophases
    • edited by K. Holmberg, John Wiley & Sons, Ltd.
    • S. T. Hyde, Identification of lyotropic liquid crystalline mesophases, Handbook of applied surface and colloid chemistry, edited by K. Holmberg, John Wiley & Sons, Ltd., 2001.
    • (2001) Handbook of Applied Surface and Colloid Chemistry
    • Hyde, S.T.1
  • 15
    • 3042888500 scopus 로고    scopus 로고
    • Construction of triply periodic minimal surfaces
    • MR 97i:53008
    • H. Karcher and K. Poltier, Construction of triply periodic minimal surfaces, Phil. Trans. R. Soc. Lond. A (1996) 354, 2077-2104. MR 97i:53008
    • (1996) Phil. Trans. R. Soc. Lond. A , vol.354 , pp. 2077-2104
    • Karcher, H.1    Poltier, K.2
  • 16
    • 84972496748 scopus 로고
    • The structure of complete embedded surfaces with constant mean curvature
    • MR 90g:53011
    • N. Korevaar, R. Kusner, and B. Solomon, The structure of complete embedded surfaces with constant mean curvature, J. Diff. Geom. 30 (1989), 465-503. MR 90g:53011
    • (1989) J. Diff. Geom. , vol.30 , pp. 465-503
    • Korevaar, N.1    Kusner, R.2    Solomon, B.3
  • 17
    • 1842791621 scopus 로고    scopus 로고
    • Periodic minimal surfaces of cubic symmetry
    • E. A. Lord and A. L. Mackay, Periodic minimal surfaces of cubic symmetry, Current Science, 85 (2003), 346-362.
    • (2003) Current Science , vol.85 , pp. 346-362
    • Lord, E.A.1    Mackay, A.L.2
  • 18
    • 1842640337 scopus 로고    scopus 로고
    • The Bilbao Crystallographic Server: A web site with crystallographic tools using the International Tables for Crystallography
    • Praha, Czech Republic
    • E. Kroumova, J. M. Perez-Mato, M. I. Aroyo, S. Ivantchev, G. Madariaga, and H. Wondratschek, The Bilbao Crystallographic Server: a web site with crystallographic tools using the International Tables for Crystallography, 18th European Crystallographic Meeting, Praha, Czech Republic (1998), http://www.cryst.ehu.es.
    • (1998) 18th European Crystallographic Meeting
    • Kroumova, E.1    Perez-Mato, J.M.2    Aroyo, M.I.3    Ivantchev, S.4    Madariaga, G.5    Wondratschek, H.6
  • 19
    • 1842690836 scopus 로고
    • Scola de Geometria Diferencial, Universidade Federal do Ceará (Brazil)
    • W. H. Meeks III, Lectures on Plateau's problem, Scola de Geometria Diferencial, Universidade Federal do Ceará (Brazil), 1978.
    • (1978) Lectures on Plateau's Problem
    • Meeks III, W.H.1
  • 20
    • 0344928071 scopus 로고    scopus 로고
    • Regularity of isoperimetric hypersurfaces in Riemannian manifolds
    • F. Morgan, Regularity of isoperimetric hypersurfaces in Riemannian manifolds, Trans. Amer. Math. Soc., 355 (2003), 5041-5052.
    • (2003) Trans. Amer. Math. Soc. , vol.355 , pp. 5041-5052
    • Morgan, F.1
  • 21
    • 1842741175 scopus 로고    scopus 로고
    • preprint
    • n, preprint (2003).
    • (2003) n
  • 22
    • 0001192899 scopus 로고    scopus 로고
    • Some sharp isoperimetric theorems for Riemannian manifolds
    • MR 2002e:53043
    • F. Morgan and D. L. Johnson, Some sharp isoperimetric theorems for Riemannian manifolds, Indiana Univ. Math. J. 49 (2000), 1017-1041. MR 2002e:53043
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 1017-1041
    • Morgan, F.1    Johnson, D.L.2
  • 23
    • 0035154765 scopus 로고    scopus 로고
    • The invariant cubic rod (cylinder) packings: Symmetries and coordinates
    • MR 2001m:52033
    • M. O'Keeffe, J. Plévert, Y. Teshima, Y. Watanabe, and T. Ogawa, The invariant cubic rod (cylinder) packings: symmetries and coordinates, Acta Cryst. A57 (2001), 110-111. MR 2001m:52033
    • (2001) Acta Cryst. , vol.A57 , pp. 110-111
    • O'Keeffe, M.1    Plévert, J.2    Teshima, Y.3    Watanabe, Y.4    Ogawa, T.5
  • 24
    • 0036112164 scopus 로고    scopus 로고
    • Homogeneous cubic cylinder packings revisited
    • MR 2003c:52028
    • M. O'Keeffe, J. Plévert, and T. Ogawa, Homogeneous cubic cylinder packings revisited, Acta Cryst. A58 (2001), 125-132. MR 2003c:52028
    • (2001) Acta Cryst. , vol.A58 , pp. 125-132
    • O'Keeffe, M.1    Plévert, J.2    Ogawa, T.3
  • 25
    • 51249163412 scopus 로고
    • Stable Constant Mean Curvature Tori and the Isoperimetric Problem in Three Space Forms
    • MR 93a:53055
    • M. Ritoré and A. Ros, Stable Constant Mean Curvature Tori and the Isoperimetric Problem in Three Space Forms, Comment. Math. Helvet. 67 (1992), 293-305. MR 93a:53055
    • (1992) Comment. Math. Helvet. , vol.67 , pp. 293-305
    • Ritoré, M.1    Ros, A.2
  • 26
    • 21844487214 scopus 로고    scopus 로고
    • The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds
    • MR 96f:58038
    • _, 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. MR 96f:58038
    • (1996) Trans. Amer. Math. Soc. , vol.348 , pp. 391-410
  • 28
    • 0942306307 scopus 로고
    • Infinite periodic minimal surfaces without self-intersections
    • A. H. Schoen, Infinite periodic minimal surfaces without self-intersections, NASA Technical Note No. TN D-5541 (1970).
    • (1970) NASA Technical Note No. TN D-5541 , vol.TN D-5541
    • Schoen, A.H.1
  • 29
    • 1842741174 scopus 로고    scopus 로고
    • Bicontinuous surfaces in self-assembling amphiphilic systems
    • Morphology of Condensed Matter: Physics and Geometry of Spatially Complex Systems, edited by K. R. Mecke and D. Stoyan
    • U. S. Schwarz and G. Gompper, Bicontinuous surfaces in self-assembling amphiphilic systems, Morphology of Condensed Matter: Physics and Geometry of Spatially Complex Systems, edited by K. R. Mecke and D. Stoyan, Springer Lecture Notes in Physics, Vol. 600, pp. 107-151, 2002.
    • (2002) Springer Lecture Notes in Physics , vol.600 , pp. 107-151
    • Schwarz, U.S.1    Gompper, G.2
  • 30
    • 0024057538 scopus 로고
    • Periodic area-minimizing surfaces in block copolymers
    • E. L Thomas, D. M. Anderson, C.S. Henkee, and D. Huffman, Periodic area-minimizing surfaces in block copolymers, Nature 334 (1988), 598-602.
    • (1988) Nature , vol.334 , pp. 598-602
    • Thomas, E.L.1    Anderson, D.M.2    Henkee, C.S.3    Huffman, D.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.