Hypersurfaces with mean Curvature given by an Ambient Sobolev Function
Schätzle, Reiner
J. Differential Geom., Tome 57 (2001) no. 2, p. 371-420 / Harvested from Project Euclid
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We consider n-hypersurfaces Σj with interior Ej whose mean curvature are given by the trace of an ambient Sobolev function uj ∊ W1,p(ℝn+1) ¶ (0.1) \bar HΣj = ujνEj on Σj, ¶ where νEj denotes the inner normal of Σj. We investigate (0.1) when Σj → Σ weakly as varifolds and prove that Σ is an integral n-varifold with bounded first variation which still satisfies (0.1) for uj → u, Ej → E. p has to satisfy ¶ p > 1/2 (n + 1) ¶ and p ≥ 4/3 if n = 1. The difficulty is that in the limit several layers can meet at Σ which creates cancellations of the mean curvature.
Publié le : 2001-07-14
Classification:  
@article{1090348353,
     author = {Sch\"atzle, Reiner},
     title = {Hypersurfaces with mean Curvature given by an Ambient Sobolev Function},
     journal = {J. Differential Geom.},
     volume = {57},
     number = {2},
     year = {2001},
     pages = { 371-420},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1090348353}
}

Schätzle, Reiner. Hypersurfaces with mean Curvature given by an Ambient Sobolev Function. J. Differential Geom., Tome 57 (2001) no. 2, pp.  371-420. http://gdmltest.u-ga.fr/item/1090348353/