Pointwise curvature estimates for F-stable hypersurfaces
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 5, pp. 543-555.
@article{AIHPC_2005__22_5_543_0,
     author = {Winklmann, Sven},
     title = {Pointwise curvature estimates for $F$-stable hypersurfaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {543--555},
     publisher = {Elsevier},
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     zbl = {1088.53042},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.005/}
}
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Winklmann, Sven. Pointwise curvature estimates for $F$-stable hypersurfaces. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 5, pp. 543-555. doi : 10.1016/j.anihpc.2004.10.005. http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.005/

[1] Bernstein S., Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Math. Z. 26 (1927) 551-558. | JFM | MR

[2] Clarenz U., Sätze über Extremalen parametrischer Funktionale, Bonner Math. Schriften 322 (1999) 1-79. | MR | Zbl

[3] Clarenz U., Enclosure theorems for extremals of elliptic parametric functionals, Calc. Var. Partial Differential Equations 15 (2002) 313-324. | MR | Zbl

[4] Clarenz U., Von Der Mosel H., On surfaces of prescribed F-mean curvature, Pacific J. Math. 213 (2004) 15-36. | MR | Zbl

[5] Dierkes U., A Bernstein result for energy minimizing hypersurfaces, Calc. Var. Partial Differential Equations 1 (1993) 37-54. | MR | Zbl

[6] Dierkes U., Curvature estimates for minimal hypersurfaces in singular spaces, Invent. Math. 122 (1995) 453-473. | MR | Zbl

[7] Dierkes U., Hildebrandt S., Küster A., Wohlrab O., Minimal surfaces I, Grundlehren Math. Wiss., vol. 295, Springer, 1992. | MR | Zbl

[8] S. Fröhlich, Krümmungsabschätzungen für μ-stabile G-Minimalflächen, Dissertation, Cottbus, 2001.

[9] Fröhlich S., Curvature estimates for μ-stable G-minimal surfaces and theorems of Bernstein type, Analysis 22 (2002) 109-130.

[10] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, Springer, 1977. | MR | Zbl

[11] Heinz E., Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1952) 51-56. | MR | Zbl

[12] Jenkins H.B., On two-dimensional variational problems in parametric form, Arch. Rational Mech. Anal. 8 (1961) 181-206. | MR | Zbl

[13] Lin F.H., Estimates for surfaces which are stationary for an elliptic parametric integral, J. Partial Differential Equations 3 (1990) 78-92. | MR | Zbl

[14] Michael J.H., Simon L., Sobolev and mean-value inequalities on generalized submanifolds of R n , Comm. Pure Appl. Math. 26 (1973) 361-379. | MR | Zbl

[15] Moser J., A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960) 457-468. | MR | Zbl

[16] K. Räwer, Stabile Extremalen parametrischer Doppelintegrale in R 3 , Dissertation, Bonn, 1993. | Zbl

[17] Sauvigny F., Curvature estimates for immersions of minimal surface type via uniformization and theorems of Bernstein type, Manuscripta Math. 67 (1990) 67-97. | MR | Zbl

[18] Schoen R., Estimates for stable minimal surfaces in three dimensional manifolds, in: Bombieri E. (Ed.), Seminar on Minimal Submanifolds, Ann. Math. Stud., vol. 103, 1983, pp. 111-126. | MR | Zbl

[19] Schoen R., Simon L., Yau S.T., Curvature estimates for minimal hypersurfaces, Acta Math. 134 (1975) 275-288. | MR | Zbl

[20] Schoen R., Simon L., Regularity of stable minimal hypersurfaces, Comm. Pure Appl. Math. 34 (1981) 741-797. | MR | Zbl

[21] Simon L., Remarks on curvature estimates for minimal hypersurfaces, Duke Math. J. 43 (1976) 545-553. | MR | Zbl

[22] Simon L., On some extensions of Bernstein's theorem, Math. Z. 154 (1977) 265-273. | MR | Zbl

[23] White B., Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals, Invent. Math. 88 (1987) 243-256. | MR | Zbl

[24] White B., Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds, J. Differential Geom. 33 (1991) 413-443. | MR | Zbl

[25] Winklmann S., Integral curvature estimates for F-stable hypersurfaces, Calc. Var. Partial Differential Equations (2004). | MR | Zbl

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