A Convergence Theorem for Immersions with L 2 -Bounded Second Fundamental Form
Ndiaye, Cheikh Birahim ; Schätzle, Reiner
Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012), p. 235-248 / Harvested from Numdam
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Publié le : 2012-01-01
@article{RSMUP_2012__127__235_0,
     author = {Ndiaye, Cheikh Birahim and Sch\"atzle, Reiner},
     title = {A Convergence Theorem for Immersions with $L^2$-Bounded Second Fundamental Form},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {128},
     year = {2012},
     pages = {235-248},
     mrnumber = {2978007},
     zbl = {1254.53091},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2012__127__235_0}
}

Ndiaye, Cheikh Birahim; Schätzle, Reiner. A Convergence Theorem for Immersions with $L^2$-Bounded Second Fundamental Form. Rendiconti del Seminario Matematico della Università di Padova, Tome 128 (2012) pp. 235-248. http://gdmltest.u-ga.fr/item/RSMUP_2012__127__235_0/

[1] W. Blaschke, Vorlesungen Ueber Differentialgeometrie III, Springer (1929).

[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. | MR 1916989 | Zbl 1021.74024

[3] S. W. Hawking, Gravitational radiation in an expanding universe, J. Math. Phys., 9 (1968), pp. 598-604. | JFM 58.1412.01 | Zbl 0005.09102

[4] W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch., C28 (1973), pp. 693-703.

[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. | MR 825628 | Zbl 0561.53008

[6] E. Kuwert - R. Schätzle, Removability of point singularity of Willmore surfaces, Ann. of Math., 160, no. 1, pp. 315-357. | MR 2119722 | Zbl 1078.53007

[7] J. Langer, A compactness theorem for surfaces with L p -bounded second fundamental form, Math. Ann., 270 (1985), pp. 223-234. | MR 771980 | Zbl 0564.58010

[8] R. Schätzle, The Willmore boundary problem, Cal. Var. PDE, 37 (2010), pp. 275-302. | MR 2592972 | Zbl 1188.53006

[9] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Center for Mathematical Analysis Austrian National University, Volume 3. | MR 756417 | Zbl 0546.49019

[10] L. Simon, Existence of surfaces minimizing the Willmore functional, Comm. Anal. Geom., Vol 1, no. 2 (1993), pp. 281-326. | MR 1243525 | Zbl 0848.58012

[11] G. Thomsen, Über konforme Geometrie I: Grundlagen der Konformen Flächentheorie, Abh. Math. Sem. Hamburg (1923), pp. 31-56. | JFM 49.0530.02

[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. | MR 202066 | Zbl 0171.20001