×

Embedded, doubly periodic minimal surfaces. (English) Zbl 1031.53014

The authors study the existence of embedded doubly periodic minimal surfaces in \(\mathbb{R}^3\) and extend it to more cases.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q05 Minimal surfaces and optimization
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
PDFBibTeX XMLCite
Full Text: DOI arXiv EuDML

References:

[1] Barbosa J. L., Amer. J. Math. 98 (2) pp 515– (1976) · Zbl 0332.53006 · doi:10.2307/2373899
[2] Courant R., Dirichlet’s principle, conformal mapping, and minimal surfaces (1950) · Zbl 0040.34603
[3] Dierkes U., Minimal surfaces, I: Boundary value problems (1992) · Zbl 0777.53012
[4] Gilbarg D., Elliptic partial differential equations of second order, (1983) · Zbl 0562.35001
[5] Jenkins H., Arch. Rational Mech. Anal. 21 pp 321– (1966)
[6] Karcher H., Geometry and topology of submanifolds, III (Leeds, 1990) pp 174– (1991)
[7] Karcher, H. and Polthier, K. 1993. [Karcher and Polthier 1993], Personal communications
[8] Meeks W. H., Comment. Math. Helv. 65 (2) pp 255– (1990) · Zbl 0713.53008 · doi:10.1007/BF02566606
[9] Meeks W. H., Comment. Math. Helv. 66 (2) pp 263– (1991) · Zbl 0731.53004 · doi:10.1007/BF02566647
[10] Meeks W. H., Topology 21 (4) pp 409– (1982) · Zbl 0489.57002 · doi:10.1016/0040-9383(82)90021-0
[11] Osserman R., A survey of minimal surfaces (1969) · Zbl 0209.52901
[12] Schoen R., Seminar on minimal submanifolds pp 111– (1983)
[13] Wei F. S., Invent. Math. 109 (1) pp 113– (1992) · Zbl 0773.53005 · doi:10.1007/BF01232021
[14] Wohlgemuth M., Arch. Rational Mech. Anal. 137 (1) pp 1– (1997) · Zbl 0874.53007 · doi:10.1007/s002050050021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.