Complete Non-Orientable Minimal Surfaces in ℝ 3 and Asymptotic Behavior

Antonio Alarcón; Francisco J. López

Analysis and Geometry in Metric Spaces (2014)

  • Volume: 2, Issue: 1, page 214-234, electronic only
  • ISSN: 2299-3274

Abstract

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In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior

How to cite

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Antonio Alarcón, and Francisco J. López. " Complete Non-Orientable Minimal Surfaces in ℝ 3 and Asymptotic Behavior ." Analysis and Geometry in Metric Spaces 2.1 (2014): 214-234, electronic only. <http://eudml.org/doc/267164>.

@article{AntonioAlarcón2014,
abstract = {In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior},
author = {Antonio Alarcón, Francisco J. López},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Complete minimal surfaces; non-orientable surfaces; complete minimal surfaces},
language = {eng},
number = {1},
pages = {214-234, electronic only},
title = { Complete Non-Orientable Minimal Surfaces in ℝ 3 and Asymptotic Behavior },
url = {http://eudml.org/doc/267164},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Antonio Alarcón
AU - Francisco J. López
TI - Complete Non-Orientable Minimal Surfaces in ℝ 3 and Asymptotic Behavior
JO - Analysis and Geometry in Metric Spaces
PY - 2014
VL - 2
IS - 1
SP - 214
EP - 234, electronic only
AB - In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior
LA - eng
KW - Complete minimal surfaces; non-orientable surfaces; complete minimal surfaces
UR - http://eudml.org/doc/267164
ER -

References

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  1. [1] A. Alarcón, Compact complete minimal immersions in R3, Trans. Amer. Math. Soc., 362 (2010), pp. 4063-4076. Zbl1196.53006
  2. [2] A. Alarcón, Compact complete proper minimal immersions in strictly convex bounded regular domains of R3, AIP Conference Proceedings, 1260 (2010), pp. 105-111. 
  3. [3] A. Alarcón and F. J. López, Approximation theory for non-orientable minimal surfaces and applications. Preprint 2013, arXiv:1307.2399 (to appear in Geom. Topol.). Zbl1314.49026
  4. [4] A. Alarcón and F. J. López, Properness of associated minimal surfaces. Trans. Amer. Math. Soc., in press. Zbl1298.53011
  5. [5] A. Alarcón and F. J. López, Minimal surfaces in R3 properly projecting into R2, J. Di_erential Geom., 90 (2012), pp. 351-381. Zbl1252.53005
  6. [6] A. Alarcón and F. J. López, Compact complete null curves in Complex 3-space, Israel J. Math., 195 (2013), pp. 97-122. Zbl1288.53050
  7. [7] A. Alarcón and F. J. López, Null curves in C3 and Calabi-Yau conjectures, Math. Ann., 355 (2013), pp. 429-455.[WoS] Zbl1269.53061
  8. [8] A. Alarcón and N. Nadirashvili, Limit sets for complete minimal immersions, Math. Z., 258 (2008), pp. 107-113.[WoS] Zbl1167.53007
  9. [9] L. Ferrer, F. Martín, and W. H. Meeks, III, Existence of proper minimal surfaces of arbitrary topological type, Adv. Math., 231 (2012), pp. 378-413.[WoS] Zbl1246.53006
  10. [10] F. Martín and N. Nadirashvili, A Jordan curve spanned by a complete minimal surface, Arch. Ration. Mech. Anal., 184 (2007), pp. 285-301.[WoS] Zbl1114.49039
  11. [11] W. H. Meeks, III, The classi_cation of complete minimal surfaces in R3 with total curvature greater than −8_, Duke Math. J., 48 (1981), pp. 523-535. 
  12. [12] W. H. Meeks, III and S. T. Yau, The classical Plateau problemand the topology of three-dimensionalmanifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn’s lemma, Topology, 21 (1982), pp. 409-442. Zbl0489.57002
  13. [13] H. Minkowski, Volumen und Oberfläche, Math. Ann., 57 (1903), pp. 447-495. 
  14. [14] N. Nadirashvili, Hadamard’s and Calabi-Yau’s conjectures on negatively curved and minimal surfaces, Invent. Math., 126 (1996), pp. 457-465. Zbl0881.53053
  15. [15] R. Schoen and S. T. Yau, Lectures on harmonic maps, Conference Proceedings and Lecture Notes in Geometry and Topology, II, International Press, Cambridge, MA, 1997. Zbl0886.53004

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