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Experimental Mathematics Volume 27, 2018 - Issue 1
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Original Articles

Higher Genus Doubly Periodic Minimal Surfaces

Peter ConnorDepartment of Mathematical Sciences, Indiana University South Bend, South Bend, IN, USACorrespondence[email protected]
Pages 47-61 | Published online: 14 Oct 2016

References

  • [Baginski and Ramos-Batista 11] F. Baginski and V. Ramos-Batista. “Solving Period Problems for Minimal Surfaces with the Support Function.” Adv. Appl. Math. Sci. 9 (2011), 85–114.
  • [Connor and Weber 12] P. Connor and M. Weber. “The Construction of Doubly Periodic Minimal Surfaces via Balance Equations.” Am. J. Math. 134 (2012), 1275–1301.
  • [Douglas 14] C. Douglas. “Genus One Scherk Surfaces and Their Limits.” J. Differ. Geom. 1 (2014), 1–59.
  • [Hauswirth and Traizet 02] L. Hauswirth and M. Traizet. “The Space of Embedded Doubly-Periodic Minimal Surfaces.” Indiana Univ. Math. J. 51:5 (2002), 1041–1080.
  • [Karcher 88] H. Karcher. “Embedded Minimal Surfaces Derived from Scherk’s Examples.” Manuscripta Math. 62 (1988), 83–114.
  • [Lazard-Holly and Meeks 01] H. Lazard-Holly and W.H. Meeks III. “Classification of Doubly-Periodic Minimal Surfaces of Genus Zero.” Inventiones Mathematicae 143 (2001), 1–27.
  • [Meeks and Rosenberg 88] W. H. Meeks III and H. Rosenberg. “The Geometry, Topology, and Existence of Doubly Periodic Minimal Surfaces.” C. R. Acad. Sci. Paris 306 (1988), 605–609. Research Announcement.
  • [Meeks and Rosenberg 89] W. H. Meeks III and H. Rosenberg. “The Global Theory of Doubly Periodic Minimal Surfaces.” Inventiones Math. 97 (1989), 351–379.
  • [Pérez et al. 07] J. Pérez, M. Rodriguez, and M. Traizet. “The Classification of Doubly Periodic Minimal Tori with Parallel Ends.” J. Diff. Geom. 69 (2007), 523–577.
  • [Ramos-Batista 02] V. Ramos-Batista. “The Doubly Periodic Costa Surfaces.” Math. Z. 240 (2002), 549–577.
  • [Rossman et al. 00] W. Rossman, E. Thayer, and M. Wohlgemuth. “Embedded, Doubly Periodic Minimal Surfaces.” Exp. Math. 9:2 (2000), 197–219.
  • [Scherk 35] H. F. Scherk. “Bemerkungen über die kleinste Fläche Innerhalb gegebener Grenzen.” J. R. Angew. Math. 13 (1835), 185–208.
  • [Weber and Wolf 12] M. Weber and M. Wolf. “Handle Addition for Doubly-Periodic Scherk Surfaces.” J. für die Reine Angew. Math. 2012 (2012), 175–216.
  • [Wei 92] F. Wei. “Some Existence and Uniqueness Theorems for Doubly Periodic Minimal Surfaces.” Invent. Math. 109 (1992), 113–136.

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