|
Adding Handles to the Helicoid
Author(s):
David
Hoffman;
Fusheng
Wei;
Hermann
Karcher
Journal:
Bull. Amer. Math. Soc.
29
(1993),
77-84.
MSC (2000):
Primary 53A10;
Secondary 58E12, 49Q06
MathSciNet review:
1193537
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- *
- {chh1}M.~Callahan, D.~Hoffman, and J.~Hoffman, {\it Computer graphics tools for the study of minimal surfaces\/},Comm. ACM {\bf 31} (1988), 648--661. MR 945033
- *
- {co2}C.~Costa, {\it Example of a complete minimal immersion in {$\bfR^3$} of genus one and three embedded ends\/},Bol. Soc. Brasil. Mat. {\bf 15} (1984), 47--54. MR 794728
- *
- {ho1}D.~Hoffman,{\it The discovery of new embedded minimal surfaces\,\/}: {\it elliptic functions, symmetry}\,; {\it computer graphics\/},Proceedings of the Berlin Conference on Global Differential Geometry, Lecture Notes in Math., vol. 1748, Springer-Verlag, New York,1985. MR 824068
- *
- {hm7}D.~Hoffman and W.~H. Meeks~III,{\it Embedded minimal surfaces of finite topology\/}, Ann. of Math. (2) {\bf 131} (1990), 1--34. MR 1038356
- *
- {hm11}\bysame, {\it Minimal surfaces based on the catenoid\/},Amer. Math. Monthly, Special Geometry Issue {\bf 97} (1990), 702--730. MR 1072813
- *
- {hw1}D.~Hoffman and M.~Wohlgemuth,{\it Limiting behavior of classical periodic minimal surfaces\/},GANG preprint series III (to appear). MR
- *
- {h2}J.~T. Hoffman,{\it M{ESH} manual\/},{GANG preprint series II, \#35}. MR
- *
- {ka7}H.~Karcher,{\it Embedded minimal surfaces derived from {S}cherk\RM's examples\/}, {Manuscripta Math.} {\bf 62} (1988), 83--114. MR 958255
- *
- {lor1}F.~J. Lopez and A.~Ros, {\it On embedded complete minimal surfaces of genus zero\/},{J. Differential Geom.} {\bf 33} (1991), 293--300. MR 1085145
- *
- {mr3}W.~H. Meeks~III and H.~Rosenberg,{\it The global theory of doubly periodic minimal surfaces\/},{Invent. Math.} {\bf 97} (1989), 351--379. MR 1001845
- *
- {ni2}J.~{C.}~{C.} Nitsche, {\em Lectures on minimal surfaces}, vol.1, Cambridge Univ. Press, Cambridge, 1989. MR 1015936
- *
- {os3}R.~Osserman,{\it Global properties of minimal surfaces in {$E^3$} and {$E^n$}\/},{Ann. of Math.} (2) {\bf 80} (1964), 340--364. MR 179701
- *
- {os1}\bysame, {\em A survey of minimal surfaces},2nd ed., Dover, New York, 1986. MR 852409
- *
- {pet}I.~Peterson,{\it Three bites in a doughnut\/},{Sci. News} {\bf 127} (1985), 168--169. MR
- *
- {sche1}H.~F. Scherk,{\it Bemerkungen \"{u}ber die kleinste fl\"{a}che innerhalb gegebener grenzen\/},{J. Reine Angew. Math.} {\bf 13} (1835), 185--208. MR
- *
- {sc1}R.~Schoen,{\it Uniqueness, symmetry, and embeddedness of minimal surfaces\/},J. Differential Geom. {\bf 18} (1983), 791--809. MR 730928
- *
- {wei2}F.~Wei,{\it Some existence and uniqueness theorems for doubly periodic minimal surfaces\/},{Invent. Math.} {\bf 109} (1992), 113--136. MR 1168368
- *
- {w2}M.~Wohlgemuth,{\it Higher genus minimal surfaces by growing handles out of a catenoid\/},{Manuscripta Math.} {\bf 70} (1991), 397--428. MR 1092145
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
53A10, 58E12, 49Q06
Retrieve articles in all Journals with MSC
(2000):
53A10, 58E12, 49Q06
Additional Information:
DOI:
10.1090/S0273-0979-1993-00401-4
PII:
S 0273-0979(1993)00401-4
|
