MINIMAL SURFACES COMPILED BY HOJOO LEE ([email protected]) LAST UPDATED ON 15 JUNE 2017. 56 Books + 25 ICM Reports + 41 Expository Articles & Surveys RIEMANN’S MINIMAL SURFACE IN R3. http://www.indiana.edu/˜minimal/archive/ 1 2 MINIMALSURFACES I. BOOKS &MONOGRAPHS 2012 A theory of branched minimal surfaces Tromba, Anthony Springer Monographs in Mathematics. Springer, Heidelberg, 2012. x+191 pp. 2011 A course in minimal surfaces Colding, Tobias Holck; Minicozzi, William P., II Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp. 2011 Minimal submanifolds in pseudo-Riemannian geometry. Anciaux, Henri With a foreword by F. Urbano. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011. xvi+167 pp. 2010 Discrete constant mean curvature surfaces via conserved quanti- ties Rossman, Wayne COE Lecture Note, 25. Math-for-Industry Lecture Note Series. Kyushu University, Fac- ulty of Mathematics, Fukuoka, 2010. 2010 Geometric measure theory and minimal surfaces Bombieri, E. (Ed.) Lectures from the Centro Internazionale Matematico Estivo (C.I.M.E.) Summer School held in Varenna, August 24 – September 2, 1972. Edited by E. Bombieri. Reprint of the 1973 original. Centro Internazionale Matematico Estivo (C.I.M.E.) Summer Schools, 61. Springer, Heidelberg; Fondazione C.I.M.E., Florence, 2010. iv+230 pp. MINIMALSURFACES 3 2010 Global analysis of minimal surfaces Dierkes, Ulrich; Hildebrandt, Stefan; Tromba, Anthony J. Revised and enlarged second edition. Grundlehren der Mathematischen Wissenschaften, 341. Springer, Heidelberg, 2010. xvi+537 pp. 2010 Minimal surfaces Dierkes, Ulrich; Hildebrandt, Stefan; Sauvigny, Friedrich Revised and enlarged second edition. With assistance and contributions by A. Kuster¨ and R. Jakob. Grundlehren der Mathe- matischen Wissenschaften, 339. Springer, Heidelberg, 2010. xvi+688 pp. 2010 Regularity of minimal surfaces Dierkes, Ulrich; Hildebrandt, Stefan; Tromba, Anthony J. Revised and enlarged second edition. With assistance and contributions by A. Kuster.¨ Grundlehren der Mathematischen Wis- senschaften, 340. Springer, Heidelberg, 2010. xviii+623 pp. 2007 Differentialgeometrie und Minimalfl¨achen (Differential geometry and minimal surfaces) Eschenburg, Jost-Hinrich; Jost, Jurgen¨ Second edition. Springer, Berlin, 2007. xvi+256 pp. 2006 Finiteness of the set of solutions of Plateau’s problem for polyg- onal boundary curves Jakob, Ruben Bonner Mathematische Schriften, 379. Universitat¨ Bonn, Mathematisches Institut, Bonn, 2006. iv+95 pp. 4 MINIMALSURFACES 2003 Minimal submanifolds and related topics Xin, Yuanlong Nankai Tracts in Mathematics, 8. World Scientific Publishing Co., Inc., River Edge, NJ, 2003. viii+262 pp. 2003 Surfaces with constant mean curvature Kenmotsu, Katsuei Translated from the 2000 Japanese original by Katsuhiro Moriya and revised by the au- thor. Translations of Mathematical Monographs, 221. American Mathematical Society, Providence, RI, 2003. x+142 pp. 2002 Minimal surfaces, geometric analysis and symplectic geometry Edited by Kenji Fukaya, Seiki Nishikawa and Joel Spruck Papers from the workshop and conference held at Johns Hopkins University, Baltimore, MD, March 1621, 1999. Edited by Kenji Fukaya, Seiki Nishikawa and Joel Spruck. Ad- vanced Studies in Pure Mathematics, 34. Mathematical Society of Japan, Tokyo, 2002. vi+259 pp. 2001 Constant mean curvature surfaces, harmonic maps and inte- grable systems Helein,´ Fred´ eric´ Notes taken by Roger Moser. Lectures in Mathematics ETH Zurich.¨ Birkhauser¨ Verlag, Basel, 2001. 122 pp. 2001 Global theory of minimal surfaces Edited by David Hoffman Proceedings of the Clay Mathematical Institute Summer School held in Berkeley, CA, June 25–July 27, 2001. Edited by David Hoffman. Clay Mathematics Proceedings, 2. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cam- bridge, MA, 2005. xii+800 pp. MINIMALSURFACES 5 2001 Plateau’s problem. An invitation to varifold geometry Almgren, Frederick J., Jr. Corrected reprint of the 1966 original. With forewords by Jean E. Taylor and Robert Gunning, and Hugo Rossi. Student Math- ematical Library, 13. American Mathematical Society, Providence, RI, 2001. xvi+78 pp. 2000 The mathematics of soap films: explorations with Maple Oprea, John Student Mathematical Library, 10. American Mathematical Society, Providence, RI, 2000. xiv+266 pp. 1997 Corso introduttivo alla teoria geometrica della misura ed alle superfici minime (Introduction to geometric measure theory and minimal surfaces) Ambrosio, Luigi Appunti dei Corsi Tenuti da Docenti della Scuola. Scuola Normale Superiore, Pisa, 1997. ii+144 pp. 1997 Geometry. V. Minimal surfaces Edited by Robert Osserman Encyclopaedia of Mathematical Sciences, 90. Springer-Verlag, Berlin, 1997. viii+272 pp. 1996 Lectures on minimal surfaces in R3 Fang, Yi Proceedings of the Centre for Mathematics and its Applications, Australian National University, 35. Australian National University, Centre for Mathematics and its Applica- tions, Canberra, 1996. ii+176 pp. 6 MINIMALSURFACES 1995 The index theorem for minimal surfaces of higher genus Tomi, Friedrich; Tromba, Anthony J. Mem. Amer. Math. Soc. 117 (1995), no. 560, vi+78 pp. 1994 Complete minimal surfaces of finite total curvature. Yang, Kichoon Mathematics and its Applications, 294. Kluwer Academic Publishers Group, Dordrecht, 1994. viii+157 pp. 1993 Minimal surfaces Edited by A. T. Fomenko. Translated from the Russian. Translation edited by A. B. Sossinsky. Advances in Soviet Mathematics, 15. American Mathematical Society, Providence, RI, 1993. x+342 pp. 1993 Minimal surfaces in Riemannian manifolds Ji, Min; Wang, Guang Yin Mem. Amer. Math. Soc. 104 (1993), no. 495, vi+50 pp. 1993 Value distribution theory of the Gauss map of minimal surfaces in Rm Fujimoto, Hirotaka Aspects of Mathematics, E21. Friedr. Vieweg & Sohn, Braunschweig, 1993. xiv+207 pp. MINIMALSURFACES 7 1992 Constant mean curvature immersions of Enneper type Wente, Henry C. Mem. Amer. Math. Soc. 100 (1992), no. 478, vi+77 pp. 1992 The problem of Plateau. A tribute to Jesse Douglas & Tibor Rad´o. Edited by Themistocles M. Rassias World Scientific Publishing Co., Inc., River Edge, NJ, 1992. x+335 pp. 1991 A sufficient criterion for a cone to be area-minimizing Lawlor, Gary R. Mem. Amer. Math. Soc. 91 (1991), no. 446, vi+111 pp. 1991 Elements of the geometry and topology of minimal surfaces in three-dimensional space Fomenko, A. T.; Tuzhilin, A. A. Translated from the Russian by E. J. F. Primrose. Translations of Mathematical Mono- graphs, 93. American Mathematical Society, Providence, RI, 1991. viii+142 pp. 1991 Minimal surfaces, stratified multivarifolds, and the Plateau prob- lem Dao Trong Thi; Fomenko, A. T. Translated from the Russian by E. J. F. Primrose. Translations of Mathematical Mono- graphs, 84. American Mathematical Society, Providence, RI, 1991. x+404 pp. 8 MINIMALSURFACES 1990 The Plateau problem. Part I. Historical survey. Fomenko, A. T. Translated from the Russian. Studies in the Development of Modern Mathematics, 1. Gordon and Breach Science Publishers, New York, 1990. xii+220 pp. 1990 The Plateau problem. Part II. The present state of the theory. Fomenko, A. T. Translated from the Russian. Studies in the Development of Modern Mathematics, 1. Gordon and Breach Science Publishers, New York, 1990. xii+251 pp. 1990 Variational principles of topology. Multidimensional minimal surface theory Fomenko, A. T. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1990, 374 pp. 1989 Complete and compact minimal surfaces Yang, Kichoon Mathematics and its Applications, 54. Kluwer Academic Publishers Group, Dordrecht, 1989. xii+175 pp. 1989 Lectures on minimal surfaces. Vol. 1. Introduction, fundamentals, geometry and basic boundary value problems. Nitsche, Johannes C. C. Translated from the German by Jerry M. Feinberg. With a German foreword. Cambridge University Press, Cambridge, 1989. xxvi+563 pp. MINIMALSURFACES 9 1988 Existence theorems for minimal surfaces of nonzero genus span- ning a contour Tomi, Friedrich; Tromba, Anthony J. Mem. Amer. Math. Soc. 71 (1988), no. 382, iv+83 pp. 1988 Plateau’s problem and the calculus of variations Struwe, Michael Mathematical Notes, 35. Princeton University Press, Princeton, NJ, 1988. x+148 pp. 1987 Monopoles, minimal surfaces and algebraic curves Hitchin, Nigel Seminaire´ de Mathematiques´ Superieures,´ 105. Presses de l’Universite´ de Montreal,´ Montreal, QC, 1987. 94 pp. 1986 A survey of minimal surfaces Osserman, Robert Second edition. Dover Publications, Inc., New York, 1986. vi+207 pp. 1986 Explicit determination of area minimizing hypersurfaces. II Parks, Harold R. Mem. Amer. Math. Soc. 60 (1986), no. 342, iv+90 pp. 10 MINIMAL SURFACES 1986 Equilibrium capillary surfaces Finn, Robert Grundlehren der Mathematischen Wissenschaften, 284. Springer-Verlag, New York, 1986. xvi+245 pp. 1986 Minimal surfaces in R3 Barbosa, J. Lucas M.; Colares, A. Gervasio Translated from the Portuguese. Lecture Notes in Mathematics, 1195. Springer-Verlag, Berlin, 1986. x+124 pp. 1986 Seminar on geometric measure theory Hardt, Robert; Simon, Leon DMV Seminar, 7. Birkhuser Verlag, Basel, 1986. 117 pp. 1984 Minimal surfaces and functions of bounded variation Giusti, Enrico Monographs in Mathematics, 80. Birkhauser¨ Verlag, Basel, 1984. xii+240 pp. 1984 Minimal surfaces of codimension one Massari, Umberto; Miranda, Mario North-Holland Mathematics Studies, 91. Notas de Matematica,´ 95. North-Holland Pub- lishing Co., Amsterdam, 1984. xiii+243 pp. MINIMAL SURFACES