A Convergence Theorem for Immersions with < > L 2 < >-Bounded Second Fundamental Form

Cheikh Birahim Ndiaye; Reiner Schätzle

Rendiconti del Seminario Matematico della Università di Padova (2012)

  • Volume: 127, page 235-248
  • ISSN: 0041-8994

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Ndiaye, Cheikh Birahim, and Schätzle, Reiner. "A Convergence Theorem for Immersions with &lt;$&gt;L^2&lt;$&gt;-Bounded Second Fundamental Form." Rendiconti del Seminario Matematico della Università di Padova 127 (2012): 235-248. <http://eudml.org/doc/275121>.

@article{Ndiaye2012,
author = {Ndiaye, Cheikh Birahim, Schätzle, Reiner},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {convergence theorem; immersions; Euclidean space; Möbius transformation; varifolds},
language = {eng},
pages = {235-248},
publisher = {Seminario Matematico of the University of Padua},
title = {A Convergence Theorem for Immersions with &lt;$&gt;L^2&lt;$&gt;-Bounded Second Fundamental Form},
url = {http://eudml.org/doc/275121},
volume = {127},
year = {2012},
}

TY - JOUR
AU - Ndiaye, Cheikh Birahim
AU - Schätzle, Reiner
TI - A Convergence Theorem for Immersions with &lt;$&gt;L^2&lt;$&gt;-Bounded Second Fundamental Form
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2012
PB - Seminario Matematico of the University of Padua
VL - 127
SP - 235
EP - 248
LA - eng
KW - convergence theorem; immersions; Euclidean space; Möbius transformation; varifolds
UR - http://eudml.org/doc/275121
ER -

References

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  2. [2] G. Friesecke - R. James - S. Müller, A theorem on geometric rigidity and the derivation on nonlinear plate theory from three-dimensional elasticity, Comm. Pure Appl. Math., 55, no. 11 (2002), pp. 1461–1506. Zbl1021.74024MR1916989
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  5. [5] J. E. Hutchinson, Second Fundamental Form for Varifolds and the Existence of Surfaces Minimizing Curvature. Indiana Univ. Math. J., 35, No 1 (1986), pp. 45–71. Zbl0561.53008MR825628
  6. [6] E. Kuwert - R. Schätzle, Removability of point singularity of Willmore surfaces, Ann. of Math., 160, no. 1, pp. 315–357. Zbl1078.53007MR2119722
  7. [7] J. Langer, A compactness theorem for surfaces with L p -bounded second fundamental form, Math. Ann., 270 (1985), pp. 223–234. Zbl0564.58010MR771980
  8. [8] R. Schätzle, The Willmore boundary problem, Cal. Var. PDE, 37 (2010), pp. 275–302. Zbl1188.53006MR2592972
  9. [9] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Center for Mathematical Analysis Austrian National University, Volume 3. Zbl0546.49019MR756417
  10. [10] L. Simon, Existence of surfaces minimizing the Willmore functional, Comm. Anal. Geom., Vol 1, no. 2 (1993), pp. 281–326. Zbl0848.58012MR1243525
  11. [11] G. Thomsen, Über konforme Geometrie I: Grundlagen der Konformen Flächentheorie, Abh. Math. Sem. Hamburg (1923), pp. 31–56. Zbl49.0530.02JFM49.0530.02
  12. [12] T. J. Willmore, Note on embedded surfaces, Ann. Stiint. Univ. Al. I. Cuza Iasi, Sect. Ia Mat. (N. S) 11B (1965), pp. 493–496. Zbl0171.20001MR202066

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