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Bibliography Bibliography The foliowing references are not eomplete with respect to the early literature but cover only some of the essential papers. A very detailed and essentially eomplete bibliography of the literature on two-dimensional minimal surfaces until1970 is given in Nitsehe's treatise [28] (cf. also Nitsche [37]). Nitsehe's bibliography is partieularly helpful for the historically interested reader as eaeh of its more than 1200 items is diseussed or at least brielly mentioned in the right eontext, and the page numbers attaehed to eaeh bibliographie referenee make it very easy to loeate the eorresponding diseussion. We have tried to eolleet as mueh as possible of the more recent literature and to inelude some eross-references to adjacent areas; eompleteness in the latter direction has neither been aspired nor attained. We partieularly refer the reader to the following Lecture notes: MSG: Minimal submanifolds and geodesics. Proceedings of the Japan-United States Seminar on Minimal Submanifolds, including Geodesies, Tokyo 1977, Kagai Publications, Tokyo 1978 SOG: Seminar on Differential Geometry, edited by S.T. Yau, Ann. Math. Studies 102, Princeton 1982 SMS: Seminar on Minimal Submanifolds, edited by Enrieo Bombieri. Ann. Math. Studies 103, Princeton 1983 TVMA: Theorie des variete minimales et applieations. seminaire Palaiseau, oet. 1983-juin 1984. Asterisque 154-155 (1987) CGGA: Computer Graphics and Geometrie Analysis. Proceedings ofthe Conference on Differential Geometry, Calculus ofVariations and Computer Graphies, edited by P. Coneus, R. Finn, D.A. Hoffman. Math. Sei. Res. Inst. Conferenee Proe. Series Nr. 17. Springer, New York 1990 We also refer to the following report by H. Rosenberg which appeared in May 1992; therefore its bibliographieal references are not included in our bibliography: Rosenberg, H. Some recent developments in the theory of properly embedded minimal surfaces in 1R3• Seminaire BOURBAKI, no. 759 (1992), 64 pp. Abikoff, W. 1. The real analytie theory ofTeiehmüller spaee. Leet. Notes Math. 820. Springer, Berlin Heidelberg New York 1980 Abreseh, U. 1. Constant mean eurvature tori in terms of elliptie funetions. J. Reine Angew. Math. 374, 169-192 (1987) Adam,N.K. 1. The physics and ehemistry ofsurfaces. 3rd. edn. Oxford Univ. Press, London 1941 2. The molecular meehanism of eapillary phenomena. Nature 115, 512-513 (1925) Adams, R.A. 1. Sobolev spaces. Academie Press, New York 1975 Adamson, A.W. 1. Physical ehemistry of surfaces. 2nd edn. Interscience, New York 1967 342 Bibliography Agmon, S., Douglis, A., Nirenberg, L. 1. Estimates near the boundary for solutions of elliptic ditTerential equations satisfying general boundary eonditions I. Commun. Pure Appl. Math. 12, 623-727 (1959) 2. Estimates near the boundary for solutions of elIiptie ditTerential equations satisfying general boundary eonditions H. Commun. Pure Appl. Math. 17,35-92 (1964) Ahlfors, L. 1. On quasieonformal mappings. J. Anal. Math. 4,1-58 (1954) 2. The eomplex analytie strueture on the space of c10sed Riemann surfaces. In: Analytie funetions. Princeton Univ. Press, 1960 3. Curvature properties ofTeiehmüller's spaee. J. Anal. Math. 9,161-176 (1961) 4. Some remarks on Teiehmüller's space of Riemann surfaces. Ann. Math. (2) 74, 171-191 (1961) 5. Complex analysis. McGraw-Hill, New Vork 1966 6. Conformal invariants. McGraw-Hill, New Vork 1973 Ahlfors, L., Bers, L. 1. Riemann's mapping theorem for variable metries. Ann. Math. (2) 72, 385-404 (1960) Ahlfors, L., Sario L. 1. Riemann surfaces. Ann. Math. Stud., Princeton Univ. Press, Princeton 1960 Alexander, H., HotTman, D., Osserman, R. 1. Area estimates for submanifolds of euelidean spaee. INDAM Sympos. Math. 14,445-455 (1974) Alexander, H., Osserman, R. 1. Area bounds for various elasses of surfaces. Am. J. Math. 97, 753-769 (1975) AlexandrotT, P., Hopf, H. 1. Topologie. Erster Band. Springer, Berlin 1935 Allard, W.K. 1. On the first variation of a varifold. Ann. Math. (2) 95, 417-491 (1972) 2. On the first variation of a manifold: boundary behavior. Ann. Math. 101,418-446 (1975) Allard, W.K., Almgren, F.J. 1. Geometrie measure theory and the ealeulus of variations. Proceedings of Symposia in Pure Mathematics 44. Amer. Math. Soe., Providenee 1986 Almgren, F.J. 1. Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem. Ann. Math. (2) 84, 277-292 (1966) 2. Plateau's problem. An invitation to varifold geometry. Benjamin, New Vork 1966 3. Existence and regularity alm ost everywhere of solutions to elIiptie variational problems with eonstraints. Mem. Am. Math. Soe. 4, no. 165 (1976) 4. The theory of varifolds; a variational ealeulus in the large for the k-dimensional area integrand. Mimeographed Notes, Princeton 1965 5. Minimal surfaee forms. Math. IntelIigencer 4, 164-172 (1982) 6. Q-valued funetions minimizing Diriehlet's integral and the regularity of area minimizing reetifiable eurrents up to codimension two. Bull. Am. Math. Soe. 8, 327-328 (1983) and typoscript, 3 vols, Princeton University 7. Optimal isoperimetrie inequalities. Indiana Univ. J. 35, 451-547 (1986) Almgren, F.J., Simon, L. 1. Existence of embedded solutions of Plateau's problem. Ann. Se. Norm. Super. Pisa CI. Sei. 6, 447-495 (1979) Almgren, F.J., Super, B. 1. Multiple valued funetions in the geometrie caleulus ofvariations. Asterisque 118, 13-32 (1984) Almgren, F.J., Taylor, J.E. 1. The geometry ofsoap films and soap bubbles. Seientifie American 82-93 (1976) Almgren, F.J. Thurston, W.P. 1. Examples of unknotted eurves whieh bound only surfaces of high genus within their eonvex hulls. Ann. Math. (2) lOS, 527-538 (1977) Bibliography 343 Alt, H.W. 1. Verzweigungspunkte von H-Flächen. I. Math. Z. 127, 333-362 (1972) 2. Verzweigungspunkte von H-Flächen. H. Math. Ann. 201, 33-55 (1973) 3. Die Existenz einer Minimalfläche mit freiem Rand vorgeschriebener Länge. Arch. Ration. Mech. Anal. 51, 304-320 (1973) Alt, H.W., Tomi, F. 1. Regularity and finiteness of solutions to the free boundary problem for minimal surfaces. Math. Z. 189, 227-237 (1985) Alvarez, o. 1. Theory of strings with boundaries. NucI. Phys. B216, 125-184 (1983) Aminov, Ju.A. 1. On the instability of a minimal surface in an n-dimensional Riemannian space of constant curvature. Math. USSR, Sb. 29, 359-375 (1976) Anderson, D. 1. Studies in microstructure of microemulsions. Univ. of Minnesota, PhD thesis, 1986 Anderson, D., Henke, c., HofTman, D., Thomas, E.L. 1. Periodic area-minimizing surfaces in block copolymers. Nature 334 (6184), 598-601 (1988) Anderson, M.T. 1. The compactification of a minimal submanifold in Euc\idean space by its Gauss map. (To appear) 2. Complete minimal varieties in hyperbolic space. Invent. Math. 69, 477-494 (1982) 3. Curvature estimates for minimal surfaces in 3-manifolds. Ann. Sei. Ec. Norm. Sup. 18,89-105 (1985) Andersson, S., Hyde, S.T., Bovin, 1.0. 1. On the periodic minimal surfaces and the conductivity mechanism of rx - Agl. Z. Kristallogr. 173, 97-99 (1985) Andersson, S., Hyde, S.T., Larson, K., Lidin, S. 1. Minimal surfaces and structure: From inorganic and metal crystals to cell membranes and biopolymers. Chemical Reviews 88, 221-248 (1988) Andersson, S, Hyde, S.T., v. Schnering, H.G. 1. The intrinsic curvature of solids. Z. Kristallogr. 168, 1-17 (1984) Athanassenas, M. 1. Ein Variationsproble\TI für Flächen konstanter mittlerer Krümmung. Diplomarbeit, Bonn 1985 2. A variational problem for constant mean curvature surfaces with free boundary. J. Reine Angew. Math. 377, 97-107 (1987) Baily, W.L. 1. On the moduli of Jacobian varieties. Ann. Math. (2) 71,303-314 (1971) Bailyn, P.M. 1. Doubly-connected minimal surfaces. Trans. Am. Math. Soc. 128,206-220 (1967) Bakeiman, I. 1. Geometrie problems in quasilinear elliptic equations. Russ. Math. Surv. 25, 45-109 (1970) Bakker, G. 1. Kapillarität und Oberflächenspannung. Handbuch der Experimentalphysik, Band 6. Akad. Ver­ lagsges., Leipzig 1928 Barbosa, J.L. 1. An extrinsic rigidity theorem for minimal immersions from S2 into sn. J. DifTer. Geom. 14, 355-368 (1979) Barbosa, 1.L., DoCarmo, M.P. 1. On the size of a stable minimal surface in R 3• Am. J. Math. 98,515-528 (1976) 2. A necessary condition for a metric in Mn to be minimally immersed in R"+I. An. Acad. Bras. Cienc. SO, 451-454 (1978) 3. Stability ofminimal surfaces in spaces of constant curvature. Bol. Soc. Bras. Mat. 11, 1-10 (1980) 344 Bibliography 4. Stability ofminimal surfaces and eigenvalues ofthe Laplacian. Math. Z. 173, 13-28 (1980) 5. Helicoids, catenoids, and minimal hypersurfaces of R 3 invariant by an P-parameter group of motions. An. Acad. Bras. Cienc. 53, 403-408 (1981) 6. Stability of hypersurfaces with constant mean curvature. Math. Z. 185, 339- 353 (1984) Barbosa, J.L., Colares, A.G. 1. Minimal surfaces in R 3• Lect. Notes Math. 1195. Springer, Berlin Heidelberg New York 1986 Barbosa, J.L., Dajczer, M., Jorge, L.P.M. 1. Minimal ruled submanifolds in spaces of constant curvature. Indiana Univ. Math. J. 33, 531-547 (1984) Barthel, W., Volkmer, R., Haubitz, I. 1. Thomsensche Minimalflächen-analytisch und anschaulich. Result. Math. 3,129-154 (1980) Beckenbach, E.F. 1. Tbe area and boundary of minimal surfaces. Ann. Math. (2) 33, 658-664 (1932) 2. Minimal surfaces in euc1idean n-space. Am. J. Math. 55, 458-468 (1933) 3. Bloch's theorem for minimal surfaces. BuH. Am. Math. Soc. 39, 450-456 (1933) 4. Remarks on the problem of Plateau. Duke Math. J. 3, 676-681 (1937) 5. On a theorem of Fejer and Riesz. J. London Math. Soc. 13,82-86 (1938) 6. Functions having subharmonic logarithms. Duke Math. J. 8, 393-400 (1941) 7. Tbe analytic prolongation ofa minimal surface. Duke Math. J. 9,109-111 (1942) 8. Painleve's theorem and the analytic prolongation of minimal surfaces. Ann.
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