Isoperimetric inequalities for parametric variational problems
Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 5, p. 617-629
@article{AIHPC_2002__19_5_617_0,
     author = {Clarenz, Ulrich and von der Mosel, Heiko},
     title = {Isoperimetric inequalities for parametric variational problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {19},
     number = {5},
     year = {2002},
     pages = {617-629},
     zbl = {1014.53009},
     mrnumber = {1922471},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_5_617_0}
}
Clarenz, Ulrich; von der Mosel, Heiko. Isoperimetric inequalities for parametric variational problems. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 5, pp. 617-629. http://www.numdam.org/item/AIHPC_2002__19_5_617_0/

[1] Barbosa J.L., Do Carmo M., A proof of a general isoperimetric inequality for surfaces, Math. Z. 162 (3) (1978) 245-261. | MR 508841 | Zbl 0369.53054

[2] Beckenbach E.F., Radó T., Subharmonic functions and surfaces of negative curvature, Trans. Am. Math. Soc. 35 (1933) 662-664. | MR 1501708 | Zbl 0007.13001

[3] U. Clarenz, Enclosure theorems for extremals of elliptic parametric functionals, Calc. Var., online publication DOI 10.1007/s005260100128, 2001. | MR 1938817 | Zbl 1018.53006

[4] Clarenz U., Von Der Mosel H., Compactness theorems and an isoperimetric inequality for critical points of elliptic parametric functionals, Calc. Var. 12 (2001) 85-107. | MR 1808108 | Zbl 0968.35039

[5] Courant R., Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces, Interscience, New York, 1950. | MR 36317 | Zbl 0040.34603

[6] Dierkes U., Hildebrandt S., Küster A., Wohlrab O., Minimal Surfaces, Vol. I, Grundlehren math. Wiss., 295, Springer, Berlin, 1992. | Zbl 0777.53012

[7] Heinz E., Hildebrandt S., The number of branch points of surfaces of bounded mean curvature, J. Differential Geom. 4 (1970) 227-235. | MR 267495 | Zbl 0195.23003

[8] Hildebrandt S., Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie, Math. Z. 112 (1969) 205-213. | MR 250208 | Zbl 0175.40403

[9] Hildebrandt S., Von Der Mosel H., On two-dimensional variational problems, Calc. Var. 9 (1999) 249-267. | MR 1725204 | Zbl 0934.49022

[10] S. Hildebrandt, H. von der Mosel, Plateau's problem for parametric double integrals: I. Existence and regularity in the interior, Preprint 88 MPI f. Math. Leipzig, 2001. Preprint 745 SFB 256 Univ. Bonn, 2001, to appear in Comm. Pure. Appl. Math. | MR 1990482 | Zbl 1031.49038

[11] Sauvigny F., Introduction of isothermal parameters into a Riemannian metric by the continuity method, Analysis 19 (1999) 235-243. | MR 1715172 | Zbl 0936.35046