An existence result for minimal spheres in manifolds boundary

Edi Rosset

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 1, page 11-15
  • ISSN: 1120-6330

Abstract

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We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.

How to cite

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Rosset, Edi. "An existence result for minimal spheres in manifolds boundary." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.1 (1990): 11-15. <http://eudml.org/doc/244242>.

@article{Rosset1990,
abstract = {We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.},
author = {Rosset, Edi},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Minimal surface; Pull back; Hodge *-operator; Winding number; minimal surface; pull back; winding number; minimal sphere; 3-manifold with boundary; trivial second homotopy group},
language = {eng},
month = {2},
number = {1},
pages = {11-15},
publisher = {Accademia Nazionale dei Lincei},
title = {An existence result for minimal spheres in manifolds boundary},
url = {http://eudml.org/doc/244242},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Rosset, Edi
TI - An existence result for minimal spheres in manifolds boundary
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/2//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 1
SP - 11
EP - 15
AB - We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.
LA - eng
KW - Minimal surface; Pull back; Hodge *-operator; Winding number; minimal surface; pull back; winding number; minimal sphere; 3-manifold with boundary; trivial second homotopy group
UR - http://eudml.org/doc/244242
ER -

References

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  1. BRÉZIS, H. - CORON, J. M. - LIEB, E. H., Harmonic maps with defects. Comm. Math. Phys., 107, 1986, 649-705. Zbl0608.58016MR868739
  2. MANCINI, G. - MUSINA, R., Surfaces of minimal area enclosing a given body in R 3 . Ann. Scuola Norm. Sup. Pisa, Cl. Sci., (4), to appear. Zbl0746.49029MR1050330
  3. ROSSET, E., An analytic construction of the winding number for W 1 , n - 1 maps from S n - 1 to n-manifolds with boundary, preprint. MR1127008
  4. SACKS, J. - UHLENBECK, K., The existence of minimal immersions of 2-spheres. Ann. of Math., (2), 113, 1981, 1-24. Zbl0462.58014MR604040DOI10.2307/1971131

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